scholarly journals The cone of curves associated to a plane configuration

10.4171/cmh/5 ◽  
2005 ◽  
pp. 75-93 ◽  
Author(s):  
C. Galindo ◽  
F. Monserrat
Keyword(s):  
Cone Of Curves

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 $X$.

CONES OF CURVES AND OF LINE BUNDLES ON SURFACES ASSOCIATED WITH CURVES HAVING ONE PLACE AT INFINITY

2002 ◽  
Vol 84 (3) ◽  
pp. 559-580 ◽  
Author(s):  
ANTONIO CAMPILLO ◽  
OLIVIER PILTANT ◽  
ANA J. REGUERA-LÓPEZ
Keyword(s):  
Polyhedral Cone ◽  
Subject Classification ◽  
Factorization Theorem ◽  
Line Bundles ◽  
Unique Factorization ◽  
Primary 14C20 ◽  
New Class ◽  
Secondary 14E05 ◽  
Cone Of Curves ◽  
Projective Surfaces

Let V be a pencil of curves in ${\bf P}^2$ with one place at infinity, and $X \longrightarrow {\bf P}^2$ the minimal composition of point blow-ups eliminating its base locus. We study the cone of curves and the cones of numerically effective and globally generated line bundles on X. It is proved that all of these cones are regular. In particular, this result provides a new class of rational projective surfaces with a rational polyhedral cone of curves. The surfaces in this class have non-numerically effective anticanonical sheaf if the pencil is neither rational nor elliptic. An application is a global version on X of Zariski's unique factorization theorem for complete ideals. We also define invariants of the semigroup of globally generated line bundles on X depending only on the topology of V at infinity.2000 Mathematical Subject Classification: primary 14C20; secondary 14E05.

The cone of curves of a K3 surface

1994 ◽  
Vol 300 (1) ◽  
pp. 681-691 ◽  
Author(s):  
S�ndor J. Kov�cs
Keyword(s):  
K3 Surface ◽  
Cone Of Curves

scholarly journals Higher-dimensional foliated Mori theory

2019 ◽  
Vol 156 (1) ◽  
pp. 1-38
Author(s):  
Calum Spicer
Keyword(s):  
Minimal Model ◽  
Structure Theorem ◽  
Model Program ◽  
Minimal Model Program ◽  
Mori Theory ◽  
Higher Dimensional ◽  
Rank 2 ◽  
Cone Of Curves

We develop some foundational results in a higher-dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman–Mori cone of curves in terms of the numerical properties of $K_{{\mathcal{F}}}$ for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program (MMP) for rank 2 foliations on threefolds.

scholarly journals THE CONE OF CURVES OF FANO VARIETIES OF COINDEX FOUR

2006 ◽  
Vol 17 (10) ◽  
pp. 1195-1221 ◽  
Author(s):  
ELENA CHIERICI ◽  
GIANLUCA OCCHETTA
Keyword(s):  
Fano Varieties ◽  
Cone Of Curves

We classify the cones of curves of Fano varieties of dimension greater or equal than five and (pseudo)index dim X - 3, describing the number and type of their extremal rays.

scholarly journals The Cone of Curves of Algebraic Varieties

1984 ◽  
Vol 119 (3) ◽  
pp. 603 ◽  
Author(s):  
Yujiro Kawamata
Keyword(s):  
Algebraic Varieties ◽  
Cone Of Curves
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