Hilbert Polynomials of Kahler Differential Modules for Fat Point Schemes

被引:1
作者
Kreuzer, Martin [1 ]
Linh, Tran N. K. [2 ]
Long, Le Ngoc [1 ,2 ]
机构
[1] Univ Passau, Fak Informat & Math, D-94030 Passau, Germany
[2] Hue Univ, Univ Educ, Dept Math, 34 Le Loi, Hue, Vietnam
关键词
Fat point scheme; Kahler differential module; Hilbert function; Regularity index;
D O I
10.1007/s40306-021-00432-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given a fat point schemeW = m(1)P(1) + ... + m(s)P(s) in the projective n-space P-n over a field K of characteristic zero, the modules of Kahler differential k-forms of its homogeneous coordinate ring contain useful information about algebraic and geometric properties of W when k is an element of {1, ..., n + 1}. In this paper, we determine the value of its Hilbert polynomial explicitly for the case k = n + 1, confirming an earlier conjecture. More precisely this value is given by the multiplicity of the fat point scheme Y = (m1 - 1)P1 + ... +(m(s) - 1)P-s. For n = 2, this allows us to determine the Hilbert polynomials of the modules of Kahler differential k-forms for k = 1, 2, 3, and to produce a sharp bound for the regularity index for k = 2.
引用
收藏
页码:441 / 455
页数:15
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