Big $q$-ample Line Bundles

Details Big $q$-ample Line Bundles Big $q$-ample Line Bundles

2011-05-17

arxiv.org/abs/1105.3449v1

Mathematics

Algebraic Geometry

9 pages, 2 pdf figures

Scientific paper

A recent paper of Totaro develops a theory of $q$-ample bundles in characteristic 0. Specifically, a line bundle $L$ on $X$ is $q$-ample if for every coherent sheaf $\mathcal{F}$ on $X$, there exists an integer $m_0$ such that $m\geq m_0$ implies $H^i(X,\mathcal{F}\otimes \mathcal{O}(mL))=0$ for $i>q$. We show that a line bundle $L$ on a complex projective scheme $X$ is $q$-ample if and only if the restriction of $L$ to its augmented base locus is $q$-ample. In particular, when $X$ is a variety and $L$ is big but fails to be $q$-ample, then there exists a codimension 1 subscheme $D$ of $X$ such that the restriction of $L$ to $D$ is not $q$-ample.

Affiliated with

Also associated with

No associations

Rating

Big $q$-ample Line Bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Big $q$-ample Line Bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Big $q$-ample Line Bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727969