28 citations · 100 across the 13 of their papers we have counts for
16 papers
Computing with jets
Federico Galetto, Nicholas Iammarino
We introduce a Macaulay2 package for working with jet schemes. The main method constructs jets of ideals, polynomial rings and their quotients, ring homomorphisms, affine varieties…
Setting the scene for Betti characters
Federico Galetto
Finite group actions on free resolutions and modules arise naturally in many interesting examples. Understanding these actions amounts to describing the terms of a free resolution…
Finite group characters on free resolutions
Federico Galetto
Under reasonable assumptions, a group action on a module extends to the minimal free resolutions of the module. Explicit descriptions of these actions can lead to a better understa…
Jet Graphs
Federico Galetto, Elisabeth Helmick, Molly Walsh
We define an operation of jets on graphs inspired by the corresponding notion in commutative algebra and algebraic geometry. We examine a few graph theoretic properties and invaria…
The InvariantRing package for Macaulay2
Luigi Ferraro, Federico Galetto, Francesca Gandini +3
We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of fini…
Betti numbers of symmetric shifted ideals
Jennifer Biermann, Hernán De Alba, Federico Galetto +5
We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the…
Betti numbers of toric ideals of graphs: A case study
Federico Galetto, Johannes Hofscheier, Graham Keiper +3
We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this famil…
Distinguishing -configurations
Federico Galetto, Yong-Su Shin, Adam Van Tuyl
A -configuration is a set of points in that satisfies a number of geometric conditions. Associated to a -configuration is a sequence $(d_1…
Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies
Hiraku Abe, Lauren DeDieu, Federico Galetto +1
In this paper, we study the geometry of various Hessenberg varieties in type A, as well as families thereof, with the additional goal of laying the groundwork for future computatio…
Degrees of regular sequences with a symmetric group action
Federico Galetto, Anthony V. Geramita, David L. Wehlau
We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the vari…
The symbolic defect of an ideal
Federico Galetto, Anthony V. Geramita, Yong-Su Shin +1
Let be a homogeneous ideal of . To compare , the -th symbolic power of , with , the regular -th power, we introduce the -th sym…
On the ideal generated by all squarefree monomials of a given degree
Federico Galetto
An explicit construction is given of a minimal free resolution of the ideal generated by all squarefree monomials of a given degree. The construction relies upon and exhibits the n…
Symmetric Complete Intersections
Federico Galetto, Anthony V. Geramita, David L. Wehlau
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. W…
Propagating weights of tori along free resolutions
Federico Galetto
The action of a torus on a graded module over a polynomial ring extends to the entire minimal free resolution of the module. We explain how to determine the action of the torus on…
Free resolutions of orbit closures for the representations associated to gradings on Lie algebras of type , and
Federico Galetto
The irreducible representations of complex semisimple algebraic groups with finitely many orbits are parametrized by graded simple Lie algebras. For the exceptional Lie algebras, K…
Generators of truncated symmetric polynomials
Federico Galetto
Adem and Reichstein introduced the ideal of truncated symmetric polynomials to present the permutation invariant subring in the cohomology of a finite product of projective spaces.…