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Thursday, November 19, 2020 | History

2 edition of On the Logarithmic Kodaira dimension of affine threefolds found in the catalog.

On the Logarithmic Kodaira dimension of affine threefolds

Takashi Kishimoto

On the Logarithmic Kodaira dimension of affine threefolds

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  • 38 Currently reading

Published by Research Institute for Mathematical Sciences, Kyoto University in Kyoto, Japan .
Written in English


Edition Notes

Cover title.

Statementby Takashi Kishimoto.
SeriesRIMS -- 1435
ContributionsKyōto Daigaku. Sūri Kaiseki Kenkyūjo.
Classifications
LC ClassificationsMLCSJ 2008/00096 (Q)
The Physical Object
Pagination20 p. ;
Number of Pages20
ID Numbers
Open LibraryOL19142219M
LC Control Number2008554234

Abbreviation for "kawamata log terminal" Kodaira dimension 1. The Kodaira dimension (also called the Iitaka dimension) of a semi-ample line bundle L is the dimension of Proj of the section ring of L. 2. The Kodaira dimension of a normal variety X is the Kodaira dimension of its canonical sheaf. Kodaira vanishing theorem. The second definition I guess doesnt include the case with kodaira dimension smaller than 0 (ie -1 or -infinity depending on how you like to define it), so we're only talking about non-negative kodaira dimension. there is a book from Ueno, "Classification Theory of Algebraic Varieties and Compact Complex Spaces", and of course the book from. The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as Price: $ Zeros of log-one-forms and families of log-varieties I will introduce the result about the relation between the zeros of holomorphic log-one-forms and the log-Kodaira dimension, which is a natural generalization of Popa and Schnell's result on zeros of one-forms.


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On the Logarithmic Kodaira dimension of affine threefolds by Takashi Kishimoto Download PDF EPUB FB2

In this article, we shall consider how to analyze affine threefolds associated to the log Kodaira dimension $\overline{\kappa}$ and make the framework for this purpose under a certain geometric con Cited by: 4. If the dimension of A is 3, has log Kodaira dimension 2 and satisfies some other conditions then B cannot be of log general type.

We also show that if A and B are symplectomorphic affine varieties Author: Takashi Kishimoto. On the logarithmic Kodaira dimension of affine threefolds. International Journal of Mathematics, 17 (1), doi/SXCited by: 4.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In the theory of affine varieties In this article, we shall consider how to analyze smooth ane threefolds associated to the log Kodaira dimension and make the framework for this purpose under a certain geometric condition.

As a consequence of our result, under this geometric condition, we can describe the. On the logarithmic Kodaira dimension of affine threefolds. In this article, we shall consider how to analyze smooth ane threefolds associated to the log Kodaira dimension and make the framework for this purpose under a certain geometric condition.

As a consequence of our result, under this geometric condition, we can describe the Author: Takashi Kishimoto. ON SUBADDITIVITY OF THE LOGARITHMIC KODAIRA DIMENSION 3 In particular, if g: V → W is a dominant morphism between algebraic varieties with dimV ≤ 3, then we have the inequality (V) ≥ (F0)+ (W)where F0 is an irreducible component of a sufficiently general fiber of g: V → W.

Note that the equality ˙(X;KX +DX) = (X;KX +DX) in Corol- lary follows from the minimal model program and. The main theme of the present article is -fibrations defined on affine difference between -fibration and the quotient morphism by a G m-action is more essential than in the case of an 픸 1-fibration and the quotient morphism by a G consider necessary (and partly sufficient) conditions under which a given -fibration becomes the quotient morphism by a G m-action.

logarithmic Kodaira dimension, Nakayama’s numerical Kodaira dimension, Nakayama’s!-sheaves and b!-sheaves, and some related topics. In Section 3, we prove Theoremwhich is the main theorem of this paper. Our proof heavily depends on Nakayama’s argument in his book 19843, which is closely related to Viehweg’s covering trick and weak.

As an application, we prove the existence of nonaffine and nonproduct threefolds Y with this property by constructing a family of a certain type of open surfaces parametrized by the affine curve C. If A has dimension 3, has log Kodaira dimension 2, and satisfies some other conditions, then B cannot be of log general type.

Article information Source Duke Math. J. obtain diffeomorphic, projective threefolds of Kodaira dimensions 2, and −∞, respectively. The invariance of their Chern numbers follows as usual. Example 4: Pairs of Kodaira dimensions (0,2) and (1,3) Following [Cat78], we will describe an example of simply connected, mini-mal surface of general type with c2 1 = pg = 1.

Threefolds admitting free Ga-actions are discussed, especially a class of varieties with negative logarithmic Kodaira dimension which are total spaces of nonisomorphic Ga-bundles. Some members of the class are shown to be isomorphic as abstract varieties, but it is unknown whether any members of the class constitute counterexamples to cancellation.

The affine cancellation problem, which asks whether complex affine varieties with isomorphic cylinders are themselves isomorphic, has a positive solution for two dimensional varieties whose coordinate rings are unique factorization domains, in particular for C 2, but counterexamples are found within normal surfaces (Danielewski surfaces) and factorial threefolds of logarithmic Kodaira dimension equal to 1.

A1-ruledness of affine surfaces over non closed field Logarithmic Kodaira dimension. Let X be a smooth geometricallyconnected algebraicvariety defined overa field k of characteristiczero.

By virtue of Nagata compactification [15] and Hironaka desingularization [5] theorems, there exists an open. Let X ↪ (T, D) be a compactification of an affine 3-fold X into a smooth projective 3-fold T such that the (reduced) boundary divisor D is SNC.

In this paper, as an affine counterpart to the work due to S. Mori (cf. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. () –]), we shall classify (K + D)-negative extremal rays on T.

Iitaka,S.: On logarithmic Kodaira dimension of algebraic varieties. Complex analysis and algebraic geometry. A collection of papers dedicated to K. Kodaira, – Iwanami Shoten Publishers-Cambridge Univ.

Press, Google Scholar. The affine cancellation problem, which asks whether complex affine varieties with isomorphic cylinders are themselves isomorphic, has a positive solution for two dimensional varieties whose coordinate rings are unique factorization domains, in particular for the affine plane, but counterexamples are found within normal surfaces Danielewski surfaces and factorial threefolds of logarithmic Kodaira dimension equal to 1.

Kodaira dimension is one of the most important birational invariant in the classification theory. Let f: X → Y be a morphism between two schemes. For y ∈ Y, let X y denote the fiber of f over y ; and for a divisor D (resp.

a sheaf F) on X, let D y (resp. F y. the integral hodge conjecture for 3-folds of kodaira dimension zero - burt totaro Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites.

Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms Holomorphic forms on threefolds. In: Recent progress in arithmetic and algebraic geometry, Contemp.

Math., vol. pp. 87– of Fundamental Research Studies in Mathematics, vol. Tata Institute of Fundamental Research, Bombay, Hindustan Book Agency, New Delhi. 픸 1 *-Fibrations on Affine Threefolds (R V Gurjar, M Koras, A Galois Counterexample to Hilbert's Fourteenth Problem in Dimension Three with Rational Coefficients (Ei Kobayashi and Shigeru Kuroda) Open Algebraic Surfaces of Logarithmic Kodaira Dimension One (Hideo Kojima)Manufacturer: WSPC.

Yujiro Kawamata, Addition formula of logarithmic Kodaira dimensions for morphisms of relative dimension one, Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, ) Kinokuniya Book Store, Tokyo,pp.

– MR The whole project follows Kodaira's classification philosophy that one should develop enough classification theorems for the various $\bar\kappa$ classes and therefore (ideally) answer "all" questions about the non-compact (or affine) varieties.

Other Texts, not intended to be published $\mathbb{A}^2$-fibrations between affine spaces are trivial $\mathbb{A}^2$-bundles, arXiv Abstract. Factorial threefolds with $\mathbb{G}_a$-actions, with David R.

Finston and Parag Deepak Mehta, arXiv, (), 14p.; Variations on the log-Sarkisov program for surfaces, with Stéphane Lamy, arXiv, (), 26p. We provide infinitely many examples of pairs of diffeomorphic, non simply connected K\" ahler manifolds of complex dimension three with different Kodaira dimensions.

Also, in any possible Kodaira dimension we find infinitely many pairs of non deformation equivalent, diffeomorphic K\" ahler threefolds. complex-geometry kodaira-dimension aic-geometry kahler-manifolds share | cite | improve this question | follow | | | | asked Mar 19 '13 at In the study of projectice varieties, the Kodaira dimension is a very important invariant associated to a projective variety.

For instance, the classification of curves may completly be expressed in. Main topis include: affine varieties, their automorphisms and group actions on them, linearization problem, logarithmic Kodaira dimension, Koras-Russell threefolds and other exotic spaces, relations to A 1-homotopy, singularities, affine fibrations, planar embeddings of curves, rational curves, log uni-ruledness, log minimal model program.

A 1 ∗-fibrations on affine threefolds R. Gurjar M. Koras K. Masuda M. Miyanishi P. Russell Miyanishi's characterization of singularities appearing on A 1-fibrations does not hold in higher dimensions Takashi Kishimoto Open algebraic surfaces of logarithmic Kodaira dimension one Hideo Kojima Mariusz Koras.

Mariusz Koras (born November 10 th,Piaseczno, Poland, died September 15 th,Betina, Murter Island, Croatia) was a Polish mathematician, specializing in algebraic geometry, mainly in complex affine was also a high-altitude climber with many achievements in Tatra Mountains and Alps.

Mariusz was married with Krystyna Stańkowska-Koras and had two children. Pages from Volume (), Issue 3 by Mihnea Popa, Christian Schnell. Maeda, Hironobu.

"Classification of logarithmic Fano threefolds." On topological characterizations of complex projective spaces and affine linear spaces. Proc. Japan Acad () [22] S. Tsunoda: Open surfaces of logarithmic Kodaira dimension - ∞. Talk at Seminar on Analytic Manifolds, Univ. of Tokyo ().

Logarithmic transformations can be quite violent: they can change the Kodaira dimension, and can turn algebraic surfaces into non-algebraic surfaces. Example: Let L be the lattice Z+iZ of C, and let E be the elliptic curve C/L. Then the projection map from E×C to C is an elliptic fibration.

We will show how to replace the fiber over 0 with a. THE 14TH AFFINE ALGEBRAIC GEOMETRY MEETING On log canonical thresholds of birationally rigid Fano threefolds Abstract: The global log canonical threshold of a Fano variety is an algebraic counterpart conjecture is of course especially interesting for ffi varieties of negative logarithmic Kodaira dimension and with trivial rational.

Get this from a library. Affine algebraic geometry: proceedings of the conference, Osaka, Japan, March [Kayo Masuda; Hideo Kojima; Takashi Kishimoto; World Scientific (Firm);] -- The present volume grew out of an international conference on affine algebraic geometry held in Osaka, Japan during March and is dedicated to Professor Masayoshi Miyanishi on the occasion of.

Log Kodaira dimension of homogenous varieties / Michel Brion and De-Qi Zhang --Rational polynomials of simple type: a combinatorial proof / Pierrette Cassou-Noguès and Daniel Daigle --Locally nilpotent derviations of rings graded by an abelian group / Daniel Daigle, Gene Freudenberg and Lucy Moser-Jauslin --Explicit biregular/ birational geometry of affine threefolds: completions of A³ into del Pezzo fibrations and Mori conic bundles / Adrien.

If the surface Y is not affine, then the Kodaira dimension of X is-oo and the D-dimension is O ([Ku], Lemma ). In the second case, the canonical divisor KX =-2D and D is irreducible, so the logarithmic Kodaira dimension (Y) = 6(D + Kx: X) =-oo; in the third case, KX =-D and D is either D8 or E8.

Let. Email your librarian or administrator to recommend adding this book to your organisation's collection. Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi–Yau varieties.

Invent. Math. (3) () – [Kod63] Kodaira, K. On the Kodaira dimension of minimal threefolds. Math. Ann. (2). MAIN TOPICS INCLUDE: affine varieties, their automorphisms and group actions on them, linearization problem for reductive group actions on affine spces, logarithmic Kodaira dimension, completions, Koras-Russell threefolds and other exotic affine spaces, relations to A 1-homotopy, algebraic surfaces, singularities, fibrations, planar embeddings.

In continuation of the work in (4), Koras and I in (14) characterize C 2 /G, G a finite group, as a normal, affine, topologically contractible surface with negative Kodaira dimension and a unique quotient singular point. Together with recent work of Gurjar this implies that all two-dimensional quotients of affine n-space by a reductive group.

Q-homology planes with logarithmic Kodaira dimension −∞, Transformation Groups, Vol. 11, No. 4,– [15] Hideo Kojima, On the logarithmic bigenera of some affine surfaces, Affine Algebraic Geometry (edited by T.

Hibi), pp. –, Osaka Univ. Press, [16] Hideo Kojima, Logarithmic plurigenera of smooth affine.Project Euclid - mathematics and statistics online. Rotary Diffeomorphism onto Manifolds with Affine Connection Chudá, Hana, Mikeš, Josef, and Sochor, Martin, ; Smoothness of the law of manifold-valued Markov processes with jumps Picard, Jean and Savona, Catherine, Bernoulli, ; Affinity of Cherednik algebras on projective space Bellamy, Gwyn and Martino, Maurizio, Algebra & Number.[Sr91] V.

Srinivas - On the embedding dimension of an affine variety. Math. Annalen () Zbl MR [Su89] T. Sugie - Algebraic characterization of the affine plane and the affine 3-space. In: Topological methods in algebraic transformation groups (H. Kraft et al., eds.).