5 citations
6 papers · 1 filter
On ideals of minors of matrices with indeterminate entries
Mordechai Katzman
This paper has two aims. The first is to study ideals of minors of matrices whose entries are among the variables of a polynomial ring. Specifically, we describe matrices whose ide…
Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences
Mordechai Katzman, Rodney Y. Sharp
This paper is concerned with ideals in a commutative Noetherian ring of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of g…
On the arithmetic of tight closure
Holger Brenner, Mordechai Katzman
We provide a negative answer to an old question in tight closure theory by showing that the containment x^3y^3 \in (x^4,y^4,z^4)^* in K[x,y,z]/(x^7+y^7-z^7) holds for infinitely ma…
Characteristic-independence of Betti numbers of graph ideals
Mordechai Katzman
In this paper we study the Betti numbers of Stanley-Reisner ideals generated in degree 2. We show that the first six Betti numbers do not depend on the characteristic of the ground…
The rationality of the Hilbert-Kunz multiplicity in graded dimension two
Holger Brenner
We show that the Hilbert-Kunz multiplicity is a rational number for an R_+-primary homogeneous ideal I=(f_1, ..., f_n) in a two-dimensional graded domain R of finite type over an a…
Ideals in a perfect closure, linear growth of primary decompositions, and tight closure
Rodney Y. Sharp, Nicole Nossem
This paper is concerned with tight closure in a commutative Noetherian ring of prime characteristic , and is motivated by an argument of K. E. Smith and I. Swanson that show…