10 citations · 30 across the 16 of their papers we have counts for
25 papers
Positivity properties of Schur classes
Matt Larson, Alan Stapledon
Results of Fulton-Lazarsfeld and Ross-Toma show that Schur classes of ample and nef vector bundles have remarkable positivity properties. We generalize these results to a purely al…
Complementary vectors of simplicial complexes
Matt Larson, Alan Stapledon
We classify the complementary vectors of doubly Cohen-Macaulay complexes. This proves a conjecture of Swartz, negatively answers a question of Athanasiadis and Tzanaki, and gives n…
Lefschetz properties of local face modules
Matt Larson, Alan Stapledon
Local face modules are modules over face rings whose Hilbert function is the local -vector of a triangulation of a simplex. We study when Lefschetz properties hold for local fac…
Differential operators, anisotropy, and simplicial spheres
Kalle Karu, Matt Larson, Alan Stapledon
We find identities involving differential operators in the generic artinian reduction of the Stanley-Reisner ring of a simplicial sphere in any positive characteristic. These ident…
Determinants of Hodge-Riemann forms
Matt Larson, Isabella Novik, Alan Stapledon
We calculate the determinant of the bilinear form in middle degree of the generic artinian reduction of the Stanley-Reisner ring of an odd-dimensional simplicial sphere. This prove…
Equivariant Ehrhart theory, commutative algebra and invariant triangulations of polytopes
Alan Stapledon
Ehrhart theory is the study of the enumeration of lattice points in lattice polytopes. Equivariant Ehrhart theory is a generalization of Ehrhart theory that takes into account the…