Density functions for the coefficients of the Hilbert-Kunz function of polytopal monoid algebra

Abstract: We shall discuss Hilbert-Kunz density function of a Noetherian standard graded ring over a perfect field of characteristic $p>0$. We will also talk about the second coeffcient of the Hilbert-Kunz function and the possibility of existence of a $\beta$-density function for this coefficient.

Watanabe and Eto have shown that Hilbert-Kunz multiplicity of affine monoid rings with respect to a monomial ideal of finite colength can be expressed as relative volume of certain nice set arising from the convex geometry associated to the ring. In this talk, we shall discuss similar expression for the density functions of polytopal monoid algebra with respect to the homogeneous maximal ideal in terms of the associated convex geometric structure. This is a joint work with Prof. V. Trivedi. We shall also discuss the existence of $\beta$-density function for monomial prime ideals of hight one of these rings in this context.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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