Automorphic vector bundles on the stack of G-zips

Arithmetic Characteristic Classes of Automorphic Vector Bundles

We develop a theory of arithmetic characteristic classes of (fully decomposed) automorphic vector bundles equipped with an invariant hermitian metric. These characteristic classes have values in an arithmetic Chow ring constructed by means of differential forms with certain log-log type singularities. We first study the cohomological properties of log-log differential forms, prove a Poincaré le...

Chern classes of automorphic vector bundles

1.1. Suppose X is a compact n-dimensional complex manifold. Each partition I = {i1, i2, . . . , ir} of n corresponds to a Chern number c (X) = ǫ(c1(X)∪c2(X)∪. . .∪cr(X)∩[X]) ∈ Z where c(X) ∈ H(X;Z) are the Chern classes of the tangent bundle, [X] ∈ H2n(X;Z) is the fundamental class, and ǫ : H0(X;Z) → Z is the augmentation. Many invariants of X (such as its complex cobordism class) may be expres...

The Moduli Stack of G-bundles

Low Rank Vector Bundles on the Grassmannian G(1, 4)

Here we define the concept of L-regularity for coherent sheaves on the Grassmannian G(1, 4) as a generalization of Castelnuovo-Mumford regularity on Pn. In this setting we prove analogs of some classical properties. We use our notion of L-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the...

A Canonical Decomposition of Generalized Theta Functions on the Moduli Stack of Gieseker Vector Bundles

In this paper we prove a decomposition formula for generalized theta functions which is motivated by what in conformal field theory is called the factorization rule. A rational conformal field theory associates a finite dimensional vector space (called the space of conformal blocks) to a pointed nodal projective algebraic curve over C whose marked points are labelled by elements of a certain fi...