7 citations · 16 across the 9 of their papers we have counts for
9 papers
Frobenius identities for the volume map on Cohen--Macaulay rings
Karim Alexander Adiprasito, Eric Katz, Ryoshun Oba +2
We study the volume map on Artinian quotients of Cohen-Macaulay algebras in characteristic , and the interaction between it and the action of Frobenius on resolutions. This allo…
Parseval-Rayleigh identities for homogeneous complete intersections
Karim Alexander Adiprasito, Ryoshun Oba, Stavros Argyrios Papadakis +1
We prove, in any positive characteristic, Parseval-Rayleigh identities for the residue map of a homogeneous complete intersection. As an application, we give a conceptual proof of…
Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
We study semigroup algebras associated to lattice polytopes. We begin by generalizing and refining work of Hochster, and describe the volume maps of these algebras, that is, their…
The volume intrinsic to a commutative graded algebra
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
Recent works of the authors have demonstrated the usefulness of considering moduli spaces of Artinian reductions of a given ring when studying standard graded rings and their Lefsc…
The 4-Intersection Unprojection Format
Vasiliki Petrotou
Unprojection theory is a philosophy due to Miles Reid, which becomes a useful tool in algebraic geometry for the construction and the study of new interesting geometric objects suc…
Beyond positivity in Ehrhart Theory
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou +1
We study semigroup algebras arising from lattice polytopes, compute their volume polynomials (particularizing work of Hochster), and establish strong Lefschetz properties (generali…
Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles
Karim Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
We prove the hard Lefschetz property for pseudomanifolds and cycles in any characteristic with respect to an appropriate Artinian reduction. The proof is a combination of Adiprasit…
The characteristic 2 anisotropicity of simplicial spheres
Stavros Argyrios Papadakis, Vasiliki Petrotou
Assume D is a simplicial sphere, and k_1 is a field. We say that D is generically anisotropic over k_1 if, for a certain purely transcendental field extension k of k_1, a certain A…
Tom & Jerry triples with an application to Fano 3-folds
Vasiliki Petrotou
Unprojection is a theory due to Reid which constructs more complicated rings starting from simpler data. The idea of unprojection is intended for serial use. Papadakis and Neves de…