On the postulation of 0-dimensional subschemes on a smooth quadric

Salvatore Giuffrida, Renato Maggioni and Alfio Ragusa

Vol. 155 (1992), No. 2, 251–282

DOI: 10.2140/pjm.1992.155.251

Abstract

If X is a 0-dimensional subscheme of a smooth quadric Q≅P¹ × P¹ we investigate the behaviour of X with respect to the linear systems of divisors of any degree (a,b). This leads to the construction of a matrix of integers which plays the role of a Hilbert function of X; we study numerical properties of this matrix and their connection with the geometry of X. Further we relate the graded Betti numbers of a minimal free resolution of X on Q with that matrix, and give a complete description of the arithmetically Cohen-Macaulay 0-dimensional subschemes of Q.

Mathematical Subject Classification 2000

Primary: 14J25

Secondary: 14M07

Milestones

Received: 14 August 1990

Published: 1 October 1992