β-Density function on the class group of projective toric varieties

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Mondal, Mandira¹ 

[1] Chennai Math Inst, H1,SIPCOT IT Pk, Siruseri 603103, Kelambakkam, India

关键词: Coefficients of Hilbert-Kunz function;    Hilbert-Kunz density function;    beta-density function;    Projective toric variety;    Height one monomial prime ideal;    Convex geometry;   

DOI  :  10.1016/j.jpaa.2021.106845

来源: Elsevier

【 摘 要 】

We prove the existence of a compactly supported, continuous (except at finitely many points) function g(I,m) : [0, infinity) -> R for all monomial prime ideals I of R of height one where (R, m) is the homogeneous coordinate ring associated to a projectively normal toric pair (X, D), such that (0)integral(infinity) g(I,m)(lambda) d lambda = (I, M), where beta(I, m) is the second coefficient of the Hilbert-Kunz function of I with respect to the maximal ideal m, as proved by Huneke-McDermott-Monsky [u]. Using the above result, for standard graded normal affine monoid rings we give a complete description of the class map tau(m) : Cl(R) -> R introduced in [8] to prove the existence of the second coefficient of the Hilbert-Kunz function. Moreover, we show the function g(I, m) is multiplicative on Segre products with the expression involving the first two coefficients of the Hilbert plolynomial of the rings and the ideals. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free