Maximal Rank for ΩPn

Abstract

Let k an algebraically closed field and R the homogeneous coordinate ring of Pn and ΩPn the cotangent bundle of Pn. In this paper I prove that for a given set S of s general points in Pn then the evaluation map H0

Pn,ΩPn(l)

−→

s i=1 ΩPn(l)|Pi is of maximal rank. Implying that a0 = 0 or b0 = 0 so that a0b0 = 0 as conjectured by Anna Lorenzini [4, 5] see below · · · −−−→ R(−d − 2)b1

R(−d − 1)a0 −−−→ R(−d − 1)b0

R(−d)(d+n n )−s −−−→ IS −→ 0 Mathematics Subject Classification: 13D02, 16E05