Nonvanishing of conformal blocks divisors on $\bar{M}_{0,n}$
Abstract
We introduce and study the problem of finding necessary and sufficient conditions under which a conformal blocks divisor on $\bar{M}_{0,n}$ is nonzero. We give necessary conditions in type A, which are sufficient when theta and critical levels coincide. We show that divisors are subject to additive identities, dependent on ranks of the underlying bundle. These identities amplify vanishing and nonvanishing results and have other applications.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.2459
 Bibcode:
 2014arXiv1410.2459B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory;
 14H10;
 14H60;
 14N35;
 14D20;
 14C20 (primary);
 14E30 (secondary)
 EPrint:
 arXiv:1308.4906 has been broken up into two parts: p1: "Vanishing and identities of conformal blocks divisors" (Algebraic Geometry to appear) replaces arXiv:1308.4906. The present upload is p2: "Nonvanishing of conformal blocks divisors on $\bar{M}_{0,n}$". In v2, added Lemma 3.7 and removed an incorrect use of zeroth Chern class in Introduction