IJPAM: Volume 16, No. 4 (2004)

A VANISHING THEOREM FOR THE COHOMOLOGY
OF POWERS OF IDEAL SHEAVES
OF SPACE CURVES

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


Abstract.Here we show the existence of many pairs $(d,g)$ such that there is a smooth curve $C \subset {\bf {P}}^3$ with degree $d$ and genus $g$ for which we may give a reasonable upper bound for the index of regularity of every power $(\mathcal {I}_C)^k$, $k>0$. All our curves are contained in a smooth quartic surface.

Received: September 11, 2004

AMS Subject Classification: 14F17, 14H60, 14N05

Key Words and Phrases: infinitesimal neighborhoods, regularity of powers of ideal sheaves, ideal sheaves, vanishing theorems, space curves, $K3$ surface, index of regularity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 4