7 papers · 1 filter
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,…
Convex bodies and graded families of monomial ideals
Yairon Cid-Ruiz, Jonathan Montaño
We show that the mixed volumes of arbitrary convex bodies are equal to mixed multiplicities of graded families of monomial ideals, and to normalized limits of mixed multiplicities…
Analytic spread and integral closure of integrally decomposable modules
Carles Bivià-Ausina, Jonathan Montaño
We relate the analytic spread of a module expressed as the direct sum of two submodules with the analytic spread of its components. We also study a class of submodules whose integr…
Extremal growth of Betti numbers and trivial vanishing of (co)homology
Justin Lyle, Jonathan Montaño
A Cohen-Macaulay local ring satisfies trivial vanishing if for all large implies or has finite projective dimension. If satisfie…
On asymptotic vanishing behavior of local cohomology
Hailong Dao, Jonathan Montaño
Let be a standard graded algebra over a field , with irrelevant maximal ideal $\fm$, and a homogeneous -ideal. We study the asymptotic vanishing behavior of the grade…
Splittings and symbolic powers of square-free monomial Ideals
Jonathan Montaño, Luis Núñez-Betancourt
We study the symbolic powers of square-free monomial ideals via symbolic Rees algebras and methods in prime characteristic. In particular, we prove that the symbolic Rees algebra a…