Hilbert–Kunz multiplicity of binoids

Local Picard Group of Binoids and Their Algebras

Multiplicity of Resonances Equals Multiplicity of the Scattering Matrix

09 v 1 9 O ct 1 99 6 Hilbert - Kunz Functions of Cubic Curves and Surfaces

We determine the Hilbert-Kunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized Hilbert-Kunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of HilbertKunz functions of plane cubics. Combining these results with the calculation of the (generalized) Hilbert-Kunz function of Cayley’s...

The Rationality of the Hilbert-kunz Multiplicity in Graded Dimension Two

Abstract. We show that the Hilbert-Kunz multiplicity is a rational number for an R+−primary homogeneous ideal I = (f1, . . . , fn) in a twodimensional graded domain R of finite type over an algebraically closed field of positive characteristic. Moreover we give a formula for the HilbertKunz multiplicity in terms of certain rational numbers coming from the strong Harder-Narasimhan filtration of ...

Extensions of the Multiplicity

The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded k-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several directions. We discuss when these bounds are sharp, find a sharp lower bound in case of not necessarily arithmetically Cohen-Macaulay one-dimensional schemes of 3-s...