4 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…
On graphs, homology bases, and triangulated homology spheres
Karim Adiprasito, Marc Lackenby, Juan Souto +1
We describe a construction that takes as input a graph and a basis for its first homology, and returns a triangulation of a 3-dimensional homology sphere. This makes precise an ide…
-anisotropy on the moment curve for homology manifolds and cycles
Karim Adiprasito, Kaiying Hou, Daishi Kiyohara +2
We prove that the Gorensteinification of the face ring of a cycle is totally -anisotropic in characteristic . In other words, given an appropriate Artinian reduction, it cont…
All triangulations have a common stellar subdivision
Karim Adiprasito, Igor Pak
We address two longstanding open problems, one originating in PL topology, another in birational geometry. First, we prove the weighted version of Oda's \emph{strong factorization…