On partially ample divisors

2014 ◽  
Vol 287 (14-15) ◽  
pp. 1632-1641
Author(s):  
Sung Rak Choi
Keyword(s):  
Ample Divisors

ON EFFECTIVE NON-AMPLE DIVISORS

2007 ◽  
Vol 40 (1) ◽  
Author(s):  
Zbigniew Jelonek
Keyword(s):  
Ample Divisors

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 A bound on certain local cohomology modules and application to ample divisors

2001 ◽  
Vol 163 ◽  
pp. 87-106 ◽  
Author(s):  
Claudia Albertini ◽  
Markus Brodmann
Keyword(s):  
Local Cohomology ◽  
Positive Characteristic ◽  
Local Cohomology Module ◽  
Perfect Field ◽  
Noetherian Domain ◽  
Local Cohomology Modules ◽  
Generic Fibre ◽  
Cohomology Modules ◽  
Ample Divisors ◽  
Torsion Free

We consider a positively graded noetherian domain R = ⊕n∈NoRn for which R0 is essentially of finite type over a perfect field K of positive characteristic and we assume that the generic fibre of the natural morphism π: Y = Proj(R) → Y0 = Spec(R0) is geometrically connected, geometrically normal and of dimension > 1. Then we give bounds on the “ranks” of the n-th homogeneous part H2(R)n of the second local cohomology module of R with respect to R+:= ⊕m>0Rm for n < 0. If Y is in addition normal, we shall see that the R0-modules H2R+ (R)n are torsion-free for all n < 0 and in this case our bounds on the ranks furnish a vanishing result. From these results we get bounds on the first cohomology of ample invertible sheaves in positive characteristic.

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