7 papers
Subadditivity of shifts, Eilenberg-Zilber shuffle products and homology of lattices
Karim Adiprasito, Anders Björner, Joel Hakavuori +2
We show that the maximal shifts in the minimal free resolution of the quotients of a polynomial ring by a monomial ideal are subadditive as a function of the homological degree. Th…
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…
Sparse handlebody decompositions and non-finiteness of
Karim Adiprasito, Bruno Benedetti
We prove that a PL manifold admits a handle decomposition into handles of index if and only if is -stacked, i.e., it admits a PL triangulation in which all …
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…
Normal crossing immersions, cobordisms and flips
Karim Adiprasito, Gaku Liu
We study various analogues of theorems from PL topology for cubical complexes. In particular, we characterize when two PL homeomorphic cubulations are equivalent by Pachner moves b…