Paolo Lella

Minimal Castelnuovo–Mumford Regularity for a Given Hilbert Polynomial

Let K be an algebraically closed field of null characteristic and p(z) a Hilbert polynomial. We look for the minimal Castelnuovo–Mumford regularity mp(z) of closed subschemes of projective spaces over K with Hilbert polynomial p(z). Experimental evidences led us to consider the idea that mp(z) could be achieved by schemes having a suitable minimal Hilbert function. We give a constructive proof of this fact. Moreover, we are able to compute the minimal Castelnuovo–Mumford regularity mϱp(z) of schemes with Hilbert polynomial p(z) and given regularity ϱ of the Hilbert function, and also the minimal Castelnuovo–Mumford regularity mu of schemes with Hilbert function u. These results find applications in the study of Hilbert schemes. They are obtained by means of minimal Hilbert functions and of two new constructive methods which are based on the notion of growth-height-lexicographic Borel set and called ideal graft and extended lifting.

A computational approach to the ample cone of moduli spaces of curves

We present an alternate proof, much quicker and more straightforward than the original one, of the celebrated F-conjecture on the ample cone of the moduli space M¯0,n of stable rational curves with n marked points in the case n = 7.

A combinatorial description of finite O-sequences and aCM genera

The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen-Macaulay projective curves with a given degree

Rational components of Hilbert schemes

d

Segments and Hilbert schemes of points

. It is well-known that the arithmetic genus

On the functoriality of marked families

g

A Borel open cover of the Hilbert scheme

of a curve

Upgraded methods for the effective computation of marked schemes on a strongly stable ideal

C

An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme

can be easily deduced from the

THE MAXIMUM LIKELIHOOD DEGREE OF FERMAT HYPERSURFACES

h