Hilbert functions and set of points in P1×P1

In this paper we study the problem of classifying the Hilbert functions of zero-dimensional schemes in P 1 × P 1 . In particular, in the main result of the paper we give conditions to determine some Hilbert functions of set of points in P 1 × P 1 and we describe geometrically these schemes. Moreover...

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Bibliographic Details
Published inBeiträge zur Algebra und Geometrie Vol. 56; no. 1; pp. 43 - 61
Main Authors Bonacini, Paola, Marino, Lucia
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2015
Subjects
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
Original Paper
Hilbert function on
13D40
Zero-dimensional schemes
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Summary:In this paper we study the problem of classifying the Hilbert functions of zero-dimensional schemes in P 1 × P 1 . In particular, in the main result of the paper we give conditions to determine some Hilbert functions of set of points in P 1 × P 1 and we describe geometrically these schemes. Moreover, we show that the Hilbert functions of these schemes depend only on the distribution of the points on a set of ( 1 , 0 ) and ( 0 , 1 ) -lines.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-014-0212-8