1 citations · 1 across the 7 of their papers we have counts for
7 papers
Lech-Mumford constant and stability of local rings
Linquan Ma, Ilya Smirnov
We study further Mumford's notion of local semistability and, in particular, show that semistable singularities are log canonical under mild assumptions. We provide many new exampl…
Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov +1
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart po…
F-singularities of polynomials with square-free support
Aldo Conca, Alessandro De Stefani, Luis Núñez-Betancourt +1
We show that the intersection of the irreducible components of a hypersurface defined by a polynomial with square-free support has F-rational singularities in characteristic .…
The defect of the F-pure threshold
Alessandro De Stefani, Luis Núñez-Betancourt, Ilya Smirnov
Introduced by Takagi and Watanabe, the F-pure threshold is an invariant defined in terms of the Frobenius homomorphism. While it finds applications in various settings, it is prima…
Tight closure of products and F-rational singularities
Alessandro De Stefani, Ilya Smirnov
We prove a characterization of F-rationality in terms of tight closure of products of parameter ideals. Our results are inspired by the theory of complete ideals for surfaces and,…
An invitation to equimultiplicity of F-invariants
Ilya Smirnov
This note grew from the lectures I delivered at ICTP during the Summer School in honor of Hochster and Huneke. Its purpose is to provide an introduction to the notion of equimultip…
Effective generic freeness and applications to local cohomology
Yairon Cid-Ruiz, Ilya Smirnov
Let be a Noetherian domain and be a finitely generated -algebra. We study several features regarding the generic freeness over of an -module. For an ideal $I \sub…