Vector bundles with no intermediate cohomology on Fano threefolds of type $V_{22}$

Enrique Arrondo and Daniele Faenzi

Vol. 225 (2006), No. 2, 201–220

DOI: 10.2140/pjm.2006.225.201

Abstract

We classify rank-2 vector bundles with no intermediate cohomology on the general prime Fano threefold of index 1 and genus 12. The structure of their moduli spaces is given by means of a monad-theoretic resolution in terms of exceptional bundles.

Keywords

Cohen–Macaulay modules, intermediate cohomology, Fano threefolds $V_{22}$, canonical and half-canonical curves

Mathematical Subject Classification 2000

Primary: 14J60

Secondary: 14F05, 14J30, 14J45, 14D20

Milestones

Received: 12 September 2004

Revised: 7 March 2005

Accepted: 18 March 2005

Published: 1 June 2006