scholarly journals Projective klt pairs with nef anti-canonical divisor

2021 ◽  
pp. 430-464
Author(s):  
Frédéric Campana ◽  
Junyan Cao ◽  
Shin-ichi Matsumura
Keyword(s):  
Canonical Divisor

scholarly journals Images of manifolds with semi-ample anti-canonical divisor

2015 ◽  
Vol 25 (2) ◽  
pp. 273-287 ◽  
Author(s):  
Caucher Birkar ◽  
Yifei Chen
Keyword(s):  
Canonical Divisor

scholarly journals Numerical criteria for divisors on to be ample

2009 ◽  
Vol 145 (5) ◽  
pp. 1227-1248 ◽  
Author(s):  
Angela Gibney
Keyword(s):  
Moduli Space ◽  
General Type ◽  
Topological Type ◽  
Rational Curves ◽  
Canonical Divisor ◽  
Content Type ◽  
One Dimensional ◽  
Stable Curves ◽  
The One ◽  
Ample Divisors

AbstractThe moduli space $\M _{g,n}$ of n-pointed stable curves of genus g is stratified by the topological type of the curves being parameterized: the closure of the locus of curves with k nodes has codimension k. The one-dimensional components of this stratification are smooth rational curves called F-curves. These are believed to determine all ample divisors. F-conjecture A divisor on $\M _{g,n}$ is ample if and only if it positively intersects theF-curves. In this paper, proving the F-conjecture on $\M _{g,n}$ is reduced to showing that certain divisors on $\M _{0,N}$ for N⩽g+n are equivalent to the sum of the canonical divisor plus an effective divisor supported on the boundary. Numerical criteria and an algorithm are given to check whether a divisor is ample. By using a computer program called the Nef Wizard, written by Daniel Krashen, one can verify the conjecture for low genus. This is done on $\M _g$ for g⩽24, more than doubling the number of cases for which the conjecture is known to hold and showing that it is true for the first genera such that $\M _g$ is known to be of general type.

scholarly journals FINITENESS OF LOG MINIMAL MODELS AND NEF CURVES ON -FOLDS IN CHARACTERISTIC

2018 ◽  
Vol 239 ◽  
pp. 76-109
Author(s):  
OMPROKASH DAS
Keyword(s):  
Projective Variety ◽  
Smooth Projective Variety ◽  
Minimal Models ◽  
Full Generality ◽  
Canonical Divisor ◽  
Arbitrary Characteristic ◽  
Finiteness Result ◽  
Effective Divisors ◽  
Cone Of Curves ◽  
Nef Cone

In this article, we prove a finiteness result on the number of log minimal models for 3-folds in $\operatorname{char}p>5$. We then use this result to prove a version of Batyrev’s conjecture on the structure of nef cone of curves on 3-folds in characteristic $p>5$. We also give a proof of the same conjecture in full generality in characteristic 0. We further verify that the duality of movable curves and pseudo-effective divisors hold in arbitrary characteristic. We then give a criterion for the pseudo-effectiveness of the canonical divisor $K_{X}$ of a smooth projective variety in arbitrary characteristic in terms of the existence of a family of rational curves on $X$.

scholarly journals Mukai-Umemura’s example of the Fano threefold with genus 12 as a compactification of C3

1992 ◽  
Vol 127 ◽  
pp. 145-165 ◽  
Author(s):  
Mikio Furushima
Keyword(s):  
Canonical Divisor ◽  
Fano Threefold

Let (X, Y) be a smooth projective compactification with the non-normal irreducible boundary Y, namely, X is a smooth projective algebraic threefold and Y a non-normal irreducible divisor on X such that X – Y is isomorphic to C3. Then Y is ample and the canonical divisor Kx on X can be written as Kx = - r Y (1 ≦ r ≦ 4).

scholarly journals Nef anti-canonical divisors and rationally connected fibrations

2019 ◽  
Vol 155 (7) ◽  
pp. 1444-1456
Author(s):  
Sho Ejiri ◽  
Yoshinori Gongyo
Keyword(s):  
Projective Variety ◽  
Kodaira Dimension ◽  
Canonical Divisor ◽  
Complex Projective Variety ◽  
Rationally Connected ◽  
Complex Projective

We study the Iitaka–Kodaira dimension of nef relative anti-canonical divisors. As a consequence, we prove that given a complex projective variety with klt singularities, if the anti-canonical divisor is nef, then the dimension of a general fibre of the maximal rationally connected fibration is at least the Iitaka–Kodaira dimension of the anti-canonical divisor.

STABLE RANK-2 BUNDLES ON CALABI–YAU MANIFOLDS

2003 ◽  
Vol 14 (10) ◽  
pp. 1097-1120 ◽  
Author(s):  
WEI-PING LI ◽  
ZHENBO QIN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Double Cover ◽  
Stable Rank ◽  
Chern Classes ◽  
Canonical Divisor ◽  
Rank 2 ◽  
Stable Sheaves ◽  
Rank 2 Bundles ◽  
Calabi Yau Manifolds

In this paper, we apply the technique of chamber structures of stability polarizations to construct the full moduli space of rank-2 stable sheaves with certain Chern classes on Calabi–Yau manifolds which are anti-canonical divisor of ℙ1×ℙn or a double cover of ℙ1×ℙn. These moduli spaces are isomorphic to projective spaces. As an application, we compute the holomorphic Casson invariants defined by Donaldson and Thomas.

On Abelian automorphism groups of fibred surfaces of small genus

2001 ◽  
Vol 130 (1) ◽  
pp. 161-174 ◽  
Author(s):  
JIN-XING CAI
Keyword(s):  
Automorphism Group ◽  
General Type ◽  
Automorphism Groups ◽  
Projective Surface ◽  
Canonical Divisor ◽  
Smooth Projective Surface ◽  
Small Genus

It is proved that, for a complex minimal smooth projective surface S of general type with a pencil of genus g = 3 or 4, any Abelian automorphism group of S is of order [les ] 12K2S + 96(g − 1), provided K2S > 8(g − 1)2, where KS is the canonical divisor of S.

scholarly journals Stable Rationality of del Pezzo Fibrations of Low Degree Over Projective Spaces

2018 ◽  
Vol 2020 (23) ◽  
pp. 9075-9119 ◽  
Author(s):  
Igor Krylov ◽  
Takuzo Okada
Keyword(s):  
Projective Space ◽  
Three Dimensional ◽  
Projective Spaces ◽  
Canonical Divisor ◽  
Stable Rationality ◽  
Higher Dimensional ◽  
Low Degree ◽  
Del Pezzo

Abstract The main aim of this article is to show that a very general three-dimensional del Pezzo fibration of degrees 1, 2, and 3 is not stably rational except for a del Pezzo fibration of degree 3 belonging to explicitly described two families. Higher-dimensional generalizations are also discussed and we prove that a very general del Pezzo fibration of degrees 1, 2, and 3 defined over the projective space is not stably rational provided that the anti-canonical divisor is not ample.

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