Period integrals of vector bundle sections and tautological systems

On Parallel Sections of a Vector Bundle

We consider when a smooth vector bundle endowed with a connection possesses non-trivial, local parallel sections. This is accomplished by means of a derived flag of subsets of the bundle. The procedure is algebraic and rests upon the Frobenius Theorem.

The Lie Algebra of Smooth Sections of a T-bundle

In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...

Factorization of Period Integrals

Let E F be a quadratic extension of number fields. We will denote by _ the non-trivial element of the Galois group of E F and will often write _(z)=z . We will denote by U1 the unitary group in 1 variable. We assume that every Archimedean place of F splits in E. We let H0 be the unitary group for the 3_3 identity matrix. Recall that a cuspidal automorphic representation 6 of GL(3, EA) is said t...

Normalized Tautological Divisors of Semi-stable Vector Bundles

Stability of Tautological Vector Bundles on Hilbert Squares of Surfaces

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes. Let S be a smooth, projective surface, let Hilb(S) be the Hilbert scheme parametrizing subschemes of S of length 2. It is known by a classical theorem of Fogarty [Fo] that Hilb(S) is a smooth, projective variety of dimension 4. Let Z ⊂ S × H...