1 citations · 1 across the 8 of their papers we have counts for
10 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…
Absolute incidence theorems and tilings
Lukas Kühne, Matt Larson
We give a precise definition of incidence theorems in plane projective geometry and introduce the notion of ``absolute incidence theorems,'' which hold over any ring. Fomin and Pyl…
A decomposition theorem for Lefschetz modules
Omid Amini, June Huh, Matt Larson
A Lefschetz module is a module over a graded algebra that satisfies analogues of Poincaré duality, the Hard Lefschetz property, and the Hodge--Riemann relations with respect to…
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…
Fine multidegrees, universal Grobner bases, and matrix Schubert varieties
Daoji Huang, Matt Larson
We give a criterion for a collection of polynomials to be a universal Gröbner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $…
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…
Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes
Joshua Brakensiek, Manik Dhar, Jiyang Gao +2
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A specia…
Straightening laws for Chow rings of matroids
Matt Larson
We give elementary and non-inductive proofs of three fundamental theorems about Chow rings of matroids: the standard monomial basis, Poincare duality, and the dragon-Hall-Rado form…