Abstract
A recent paper of Totaro developed a theory of q-ample bundles in characteristic 0. Specifically, a line bundle L on X is q-ample if for every coherent sheaf F on X, there exists an integer m 0 such that m ≥ m 0 implies H i (X, F ⊗ 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-one subscheme D of X such that the restriction of L to D is not q-ample.
Original language | English (US) |
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Pages (from-to) | 790-798 |
Number of pages | 9 |
Journal | Compositio Mathematica |
Volume | 148 |
Issue number | 3 |
DOIs | |
State | Published - May 2012 |
Keywords
- augmented base loci
- linear series
- partial amplitude
ASJC Scopus subject areas
- Algebra and Number Theory