On the degree of the discriminant locus of a smooth hyperplane section of a threefold with non negative Kodaira dimension

1987 ◽  
Vol 48 (6) ◽  
pp. 538-542 ◽  
Author(s):  
Aldo Biancofiore
Keyword(s):  
Hyperplane Section ◽  
Kodaira Dimension ◽  
Discriminant Locus ◽  
Negative Kodaira Dimension ◽  
Smooth Hyperplane Section

scholarly journals Threefolds with negative Kodaira dimension and positive irregularity

1983 ◽  
Vol 91 ◽  
pp. 163-172 ◽  
Author(s):  
Mauro Beltrametti ◽  
Paolo Francia
Keyword(s):  
Kodaira Dimension ◽  
Complex Field ◽  
Negative Kodaira Dimension

The purpose of this paper is to study threefolds X, with negative Kodaira dimension k(X) and positive irregularity q(X), defined over the complex field C.

scholarly journals The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension

2012 ◽  
Vol 22 (2) ◽  
pp. 201-248 ◽  
Author(s):  
Sébastien Boucksom ◽  
Jean-Pierre Demailly ◽  
Mihai Păun ◽  
Thomas Peternell
Keyword(s):  
Kähler Manifold ◽  
Kodaira Dimension ◽  
Kahler Manifold ◽  
Compact Kähler Manifold ◽  
Effective Cone ◽  
Negative Kodaira Dimension

Classification of Algebraic Surfaces with Sectional Genus less than or Equal to Six. II: Ruled Surfaces with dim ϕKx⊗L(x) = l

1986 ◽  
Vol 38 (5) ◽  
pp. 1110-1121 ◽  
Author(s):  
Elvira Laura Livorni
Keyword(s):  
Line Bundle ◽  
Hyperplane Section ◽  
Ample Line Bundle ◽  
Rational Surface ◽  
Algebraic Surfaces ◽  
Sectional Genus ◽  
Rational Surfaces ◽  
Image Position ◽  
Smooth Hyperplane Section

Let L be a very ample line bundle on a smooth, connected, projective, ruled not rational surface X. We have considered the problem of classifying biholomorphically smooth, connected, projected, ruled, non rational surfaces X with smooth hyperplane section C such that the genus g = g(C) is less than or equal to six and dim where is the map associated to . L. Roth in [10] had given a birational classification of such surfaces. If g = 0 or 1 then X has been classified, see [8].If g = 2 ≠ hl,0(X) by [12, Lemma (2.2.2) ] it follows that X is a rational surface. Thus we can assume g ≦ 3.Since X is ruled, h2,0(X) = 0 andsee [4] and [12, p. 390].

THE BOGOMOLOV–MIYAOKA–YAU INEQUALITY FOR LOG CANONICAL SURFACES

2001 ◽  
Vol 64 (2) ◽  
pp. 327-343 ◽  
Author(s):  
ADRIAN LANGER
Keyword(s):  
Vector Bundles ◽  
Universal Cover ◽  
Kodaira Dimension ◽  
Projective Surface ◽  
Chern Classes ◽  
Singular Surfaces ◽  
Smooth Projective Surface ◽  
Log Canonical ◽  
Surface Singularities ◽  
Negative Kodaira Dimension

Let X be a smooth projective surface of non-negative Kodaira dimension. Bogomolov [1, Theorem 5] proved that c21 [les ] 4c2. This was improved to c21 [les ] 3c2 by Miyaoka [12, Theorem 4] and Yau [19, Theorem 4]. Equality c21 [les ] 3c2 is attained, for example, if the universal cover of X is a ball (if κ(X) = 2 then this is the only possibility). Further generalizations of inequalities for Chern classes for some singular surfaces with (fractional) boundary were obtained by Sakai [16, Theorem 7.6], Miyaoka [13, Theorem 1.1], Kobayashi [6, Theorem 2; 7, Theorem 12], Wahl [18, Main Theorem] and Megyesi [10, Theorem 10.14; 11, Theorem 0.1].In [8] we introduced Chern classes of reflexive sheaves, using Wahl's local Chern classes of vector bundles on resolutions of surface singularities. Here we apply them to obtain the following generalization of the Bogomolov–Miyaoka–Yau inequality.

scholarly journals The Chern–Ricci Flow on Oeljeklaus–Toma Manifolds

2017 ◽  
Vol 69 (1) ◽  
pp. 220-240 ◽  
Author(s):  
Tao Zheng
Keyword(s):  
Evolution Equation ◽  
Ricci Flow ◽  
Kodaira Dimension ◽  
Complex Manifolds ◽  
Hermitian Metrics ◽  
Conformal Change ◽  
Compact Complex Manifolds ◽  
Negative Kodaira Dimension

AbstractWe study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus–Toma (OT-) manifolds that are non-Kähler compact complex manifolds with negative Kodaira dimension. We prove that after an initial conformal change, the flow converges in the Gromov–Hausdorff sense to a torus with a flat Riemannianmetric determined by the OT-manifolds themselves.

scholarly journals On existence of log minimal models

2010 ◽  
Vol 146 (4) ◽  
pp. 919-928 ◽  
Author(s):  
Caucher Birkar
Keyword(s):  
Minimal Model ◽  
Kodaira Dimension ◽  
Reduction Theorem ◽  
Model Program ◽  
Minimal Models ◽  
Minimal Model Program ◽  
Log Minimal Model Program ◽  
Negative Kodaira Dimension

AbstractIn this paper, we prove that the log minimal model program in dimension d−1 implies the existence of log minimal models for effective lc pairs (e.g. of non-negative Kodaira dimension) in dimension d. In fact, we prove that the same conclusion follows from a weaker assumption, namely, the log minimal model program with scaling in dimension d−1. This enables us to prove that effective lc pairs in dimension five have log minimal models. We also give new proofs of the existence of log minimal models for effective lc pairs in dimension four and of the Shokurov reduction theorem.

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