12 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…