The Chern classes of the Verlinde bundles

Abstract

A formula for the first Chern class of the Verlinde bundle over the moduli space of smooth genus g curves is given. A finite-dimensional argument is presented in rank 2 using geometric symmetries obtained from strange duality, relative Serre duality, and Wirtinger duality together with the projective flatness of the Hitchin connection. A derivation using conformal-block methods is presented in higher rank. An expression for the first Chern class over the compact moduli space of curves is obtained.

References in corpus (4)

• The rank-level duality for non-abelian theta functions
• $s{l}_2$ conformal block divisors and the nef cone of ${\bar{M}}_{0,n}$
• The Chern character of the Verlinde bundle over the moduli space of stable curves
• Cyclic covering morphisms on ${\bar{M}}_{0,n}$

Cited by in corpus (3)

• The Chern character of the Verlinde bundle over the moduli space of stable curves
• Scaling of conformal blocks and generalized theta functions over ${\bar{M}}_{g,n}$
• Strange Duality of Verlinde spaces for G_2 and F_4