IJPAM: Volume 26, No. 4 (2006)

HOLOMORPHIC VECTOR BUNDLES ON
A FORMAL NEIGHBORHOOD OF A ${\bf {P}}^2$
INSIDE A SMOOTH $3$-FOLD WITH
NEGATIVE NORMAL BUNDLE

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $\widehat{S}$ be a formal neighborhood of ${\bf {P}}^2$ in a smooth $3$-fold with negative normal bundle and $E$ a vector bundle on $\widehat{S}$ such that $E\vert {\bf {P}}^2$ is simple. Then the local deformation space of $E$ is finite dimensional and smooth and a general element of it is ``as balanced as possible''.

Received: February 3, 2006

AMS Subject Classification: 14J60, 14D15, 13D10, 32G08, 32F10

Key Words and Phrases: exceptional variety, holomorphic vector bundle, formal complex space, local deformation space, local moduli space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 4