Zobrazeno 1 - 10
of 127
pro vyhledávání: '"De Stefani, Alessandro"'
Autor:
De Stefani, Alessandro, Smirnov, Ilya
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, in particular, the fundamental results of Lipman-Teissier and Cutkosky
Externí odkaz:
http://arxiv.org/abs/2411.03167
In this article we obtain uniform effective upper bounds for the projective dimension and the Castelnuovo-Mumford regularity of homogeneous ideals inside a standard graded polynomial ring $S$ over a field. Such bounds are independent of the number of
Externí odkaz:
http://arxiv.org/abs/2409.12787
Let $(R,\mathfrak{m})$ be a complete local ring, and $G={\rm gr}_{\mathfrak{m}}(R)$ be its associated graded ring. We introduce a homogenization technique which allows to relate $G$ to the special fiber and $R$ to the generic fiber of a "Gr\"obner-li
Externí odkaz:
http://arxiv.org/abs/2406.16421
The purpose of this note is to show that a finitely generated graded module $M$ over $S=k[x_1,\ldots,x_n]$, $k$ a field, is sequentially Cohen-Macaulay if and only if its arithmetic degree ${\rm adeg}(M)$ agrees with ${\rm adeg}(F/{\rm gin}_{revlex}(
Externí odkaz:
http://arxiv.org/abs/2307.14483
Autor:
De Stefani, Alessandro, Montaño, Jonathan, Núñez-Betancourt, Luis, Seccia, Lisa, Varbaro, Matteo
In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly $F$-regular. Furthermore, we prove that the symbolic associated graded algebra of a mixed ladder determinantal ideal is $F$-pure. The latter impl
Externí odkaz:
http://arxiv.org/abs/2305.18167
The rate of a standard graded $K$-algebra $A$ is a measure of the growth of the shifts in a minimal free resolution of $K$ as an $A$-module. In particular $A$ has rate one if and only if it is Koszul. It is known that a generic Artinian Gorenstein al
Externí odkaz:
http://arxiv.org/abs/2304.14842
Publikováno v:
Research in the Mathematical Sciences 9 (2022), Article number: 40
In this survey paper we first present the main properties of sequentially Cohen-Macaulay modules. Some basic examples are provided to help the reader with quickly getting acquainted with this topic. We then discuss two generalizations of the notion o
Externí odkaz:
http://arxiv.org/abs/2304.06609
Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring associated to th
Externí odkaz:
http://arxiv.org/abs/2210.03358
We survey results produced from the interaction between methods in prime characteristic and combinatorial commutative algebra. We showcase results for edge ideals, toric varieties, Stanley-Reisner rings, and initial ideals that were proven via Froben
Externí odkaz:
http://arxiv.org/abs/2203.09902
We study when blowup algebras are $F$-split or strongly $F$-regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals of Pfaffia
Externí odkaz:
http://arxiv.org/abs/2109.00592