10 papers
Regularity is bounded on a quasi-excellent Noetherian scheme
Alessandro De Stefani, Jack Jeffries, Nawaj KC +1
A point of a scheme has an associated tangent cone, the spectrum of a standard graded algebra encoding the local singularity. Its homological complexity can be measured by its grad…
Golod ideals in combinatorial commutative algebra
Benjamin Briggs, Trung Chau, Alessandro De Stefani
In this article we study the Golod property of standard graded algebras. We show that determinantal ideals, binomial edge ideals, and permanental ideals are Golod if and only if th…
Quadratic linear strands of prime ideals
Giulio Caviglia, Alessandro De Stefani
We prove sharp estimates on the quadratic strand of the resolution of any homogeneous prime ideal in a standard graded polynomial ring over an arbitrary field. Our bounds only depe…
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…
-injectivity does not imply -fullness in normal domains
Alessandro De Stefani, Thomas Polstra, Austyn Simpson
We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are -injective but not -full. Along the way, we find ex…
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,…