Minimal Castelnuovo-Mumford Regularity for a Given Hilbert Polynomial

作者：Cioffi F^*; Lella P; Marinari M G; Roggero M

来源：Experimental Mathematics, 2015, 24(4): 424-437.

DOI：10.1080/10586458.2015.1020577

• Borel ideal
• closed projective subscheme
• Castelnuovo-Mumford regularity
• Hilbert polynomial
• minimal function
• regularity of a Hilbert function

Let K be an algebraically closed field of null characteristic and p(z) a Hilbert polynomial. We look for the minimal Castelnuovo-Mumford regularity m(p(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 m(p(z))(rho) of schemes with Hilbert polynomial p(z) and given regularity rho of the Hilbert function, and also the minimal Castelnuovo-Mumford regularity m(u) 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.

• 出版日期2015