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
Citation
International Mathematical Forum, Vol. 6, 2011, no. 8, 389 - 398Publisher
The School of Mathematics University of Nairobi