On the Minimal Resolution Conjecture for P3

Abstract

The Minimal Resolution Conjecture that was formulated by A Lorenzini [2] has been shown to hold true for P2, P3 [3] they made use of Quadrics, here we tackle the P3 case but making use of variant methods i.e. mainly the method of Horace (m`ethode d’Horace) to evaluate sections of fibres at given points. This was introduced by A Hirschowitz in 1984 in a letter he wrote to R Hartshorne. For a general set of points P1, . . . , Pm ∈ P3, for a positive integer m, we show that the map H0 P3,ΩP3 (d + 1) −→ m i=1 ΩP3 (d + 1)|Pi is of maximal rank.