8 papers · 1 filter
Differential and symbolic powers of ideals
Alessandro De Stefani, Eloísa Grifo, Jack Jeffries
We characterize symbolic powers of prime ideals in polynomial rings over any field in terms of -linear differential operators, and of prime ideals in polynomial rings o…
Hilbert-Kunz multiplicity of powers of ideals in dimension two
Alessandro De Stefani, Shreedevi K. Masuti, Maria Evelina Rossi +1
We study the behavior of the Hilbert-Kunz multiplicity of powers of an ideal in a local ring. In dimension two, we provide answers to some problems raised by Smirnov, and give a cr…
Frobenius methods in combinatorics
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt
We survey results produced from the interaction between methods in prime characteristic and combinatorial commutative algebra. We showcase results for edge ideals, toric varieties,…
Bounds on the number of generators of prime ideals
Giulio Caviglia, Alessandro De Stefani
Let be a polynomial ring over any field , and let be a non-degenerate homogeneous prime ideal of height . When is algebraically closed, a clas…
Stability and deformation of F-singularities
Alessandro De Stefani, Ilya Smirnov
We study the problem of -adic stability of F-singularities, that is, whether the property that a quotient of a local ring by a non-zero divisor $x…
On monomial Golod ideals
Hailong Dao, Alessandro De Stefani
We study ideal-theoretic conditions for a monomial ideal to be Golod. For ideals in a polynomial ring in three variables, our criteria give a complete characterization. Over such r…