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8 papers · 2 filters
Integral closure of ideals in excellent local rings
Donatella Delfino, Irena Swanson
Let R be an excellent local ring, m its maximal ideal and I an ideal. Then there exists a positive integer c such that for all integers n, the integral closure of (I + m^n) is cont…
Cartier isomorphism for toric varieties
Manuel Blickle
In this paper I show that, just as in the smooth case, the Cartier operator induces an isomorphism on the Zariski-deRham complex of any toric variety.
Intersection multiplicities over Gorenstein rings
Claudia M. Miller, Anurag K. Singh
We construct a complex of free-modules over a Gorenstein ring R of dimension five, for which the Euler characteristic and Dutta multiplicity are different. This complex is the reso…
F-regularity does not deform
Anurag K. Singh
We show that the property of F-regularity does not deform, and thereby settle this longstanding open question in the theory of tight closure. Specifically, we construct a three dim…
Deformation of F-purity and F-regularity
Anurag K. Singh
Hochster and Huneke showed that the property of F-regularity deforms for Gorenstein rings, i.e., if (R,m) is a Gorenstein local ring such that R/tR is F-regular for some nonzerodiv…
A computation of tight closure in diagonal hypersurfaces
Anurag K. Singh
In the ring R=K[X,Y,Z]/(X^3+Y^3+Z^3), where K is a field of prime characteristic p other than 3, determining the tight closure of the ideal (X^2, Y^2, Z^2)R had existed as a classi…