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) |
|---|---|
| Pages (from-to) | 790-798 |
| Number of pages | 9 |
| Journal | Compositio Mathematica |
| Volume | 148 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 1 2012 |
| Externally published | Yes |
Keywords
- augmented base loci
- linear series
- partial amplitude
ASJC Scopus subject areas
- Algebra and Number Theory
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Brown, M. V. (2012). Big q-ample line bundles. Compositio Mathematica, 148(3), 790-798. https://doi.org/10.1112/S0010437X11007457