The stability of exceptional bundles on complete intersection $3$-folds

On Genus-1 Gromov-Witten Invariants of Complete Intersection 3-Folds

On Genus-1 Gromov-Witten Invariants of Complete Intersection 3-Folds

Notes on very ample vector bundles on 3 - folds

Let E be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of E is provided when KX+detE is nef but not big, and when a suitable positive multiple of KX+det E defines a morphism X → B with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus...

Vector Bundles on Fano 3-folds without Intermediate Cohomology

A well-known result of Horrocks (see [Ho]) states that a vector bundle on a projective space has not intermediate cohomology if and only if it decomposes as a direct sum of line bundles. There are two possible generalizations of this result to arbitrary varieties. The first one consists of giving a cohomological characterization of direct sums of line bundles. This has been done for quadrics an...

Casson invariant for Calabi - Yau 3 - folds , and bundles on K 3 fibrations

We briefly review the formal picture in which a Calabi-Yau n-fold is the complex analogue of an oriented real n-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a holomorphic Casson invariant counting bundles on a Calabi-Yau 3-fold. We develop the deformation theory necessary to obtain the virtual moduli cycles of [LT], [BF] ...