Rang maximal pour $T_P^n$

TL;DR

This paper determines the last non-trivial term of the minimal free resolution for ideals of points in projective space, confirming a conjecture for large configurations using a geometric method.

Contribution

It provides a proof of the Minimal Resolution Conjecture for large sets of points in projective space using the vectorial Horace method.

Findings

Confirmed the last non-trivial term matches the conjecture for large s

Developed a geometric proof using the vectorial Horace method

Extended understanding of minimal free resolutions of point ideals

Abstract

In this paper, I compute the last non-trivial term of the minimal free resolution of the homogeneous ideal of $s$ points of $P^n$ in sufficiently general position, for any $s$, showing that this term is the one conjectured by the Minimal Resolution Conjecture of Anna Lorenzini. I use a geometrical method, the "vectorial m\'ethode d'Horace" developped by Andr\'e Hirschowitz and Carlos Simpson to get a proof of the MRC for $s$ large enough.