Fence complexes are associated to positroid varieties, shown to be balls with matching Ehrhart and Hilbert polynomials, and positroid varieties degenerate to reduced unions of toric varieties corresponding to the complexes.
and Little, John B
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Grothendieck weights on permutohedral and matroidal fans are characterized by K-balancing, enabling a matroid-only computation of motivic Chern classes for arrangement complements in wonderful compactifications.
Frobenius identities for the volume map on Cohen-Macaulay rings give sufficient conditions for anisotropy and Hard Lefschetz in Gorenstein quotients and deduce the g-theorem for simplicial spheres plus the Ohsugi-Hibi conjecture.
Matrix representations for implicitization of rational hypersurfaces via syzygies on coefficient ideals in the Cox ring, removing the LCI-at-base-points requirement for surfaces.
Equivariant K-theory of Gieseker spaces is identified with the Jucys-Murphy center of the cyclotomic Hecke algebra.
The nth Amitsur group is a stable G-birational invariant of smooth projective G-varieties over char-0 fields for all n≥2.
A combinatorial description is given for equivariant quasicoherent sheaves on toric prevarieties.
The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.
Derives quasi-polynomial formula for local Euler characteristics on A_n singularities via toric geometry and applies it to establish hyperbolicity properties for a family of surfaces in P^3.
Quasi-F^e-splitting for all e implies numerically log canonical for numerically Q-Gorenstein normal singularities, with converse in dim 2 when p does not divide the Gorenstein index, plus a classification of 2D quasi-F-split cases.
If a smooth projective toric variety of dimension n≥2 satisfies uniform unimodularity and Thomsen stratification intersection-number conditions, then any line bundle L with L·C ≥ n-1+p on every T-invariant curve satisfies Property N_p.
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