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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

## by Takashi Kishimoto

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

Edition Notes

Cover title.

Classifications The Physical Object Statement by Takashi Kishimoto. Series RIMS -- 1435 Contributions Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. LC Classifications MLCSJ 2008/00096 (Q) Pagination 20 p. ; Number of Pages 20 Open Library OL19142219M LC Control Number 2008554234

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. V. 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.

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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 31437, 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.