On the Hilbert function on \mathbb P¹×\mathbb P¹

2010/09/21 by Paola Bonacini, Bonacini, Paola, Lucia Marino +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1009.4095

Abstract

Let Q = \mathbb P¹ x \mathbb P¹ and let X⊂ Q be a 0-dimensional scheme. This paper is a first step towards the characterization of Hilbert functions of 0- dimensional schemes in Q. In particular we show how, under some conditions on X, its Hilbert function changes when we add points to X lying on a (1,0) or (0, 1)-line. As a particular case we show also that if X is ACM this result holds without any additional hypothesis.

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