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 H0Pn,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 (118.5Kb)
Dieudonne, Laboratoir´e J. A.