173 citations · 472 across the 28 of their papers we have counts for
28 papers
Classifying Smooth Quot Schemes
Roy Skjelnes, Gregory G. Smith, Michael Stillman
The Quot scheme parametrizes the quotients of the trivial vector bundle of rank on -dimensional projective space th…
Cellular free resolutions for normalizations of toric ideals
Christine Berkesch, Lauren Cranton Heller, Gregory G. Smith +1
For any toric ideal in a polynomial ring , we provide a combinatorial description of a free resolution of the integral closure of the -module . These new complexes a…
Nonnegativity certificates on real algebraic surfaces
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
We introduce tools for transferring nonnegativity certificates for global sections between line bundles on real algebraic surfaces. As applications, we improve Hilbert's degree bou…
Simplicial complexes in Macaulay2
Ben Hersey, Gregory G. Smith, Alexandre Zotine
We highlight some features of the SimplicialComplexes package in Macaulay2.
Ramification and Discriminants of Vector Bundles and a Quick Proof of Bogomolov's Theorem
Hirotachi Abo, Robert Lazarsfeld, Gregory G. Smith
By analyzing degeneracy loci over projectivized vector bundles, we recompute the degree of the discriminant locus of a vector bundle and provide a new proof of the Bogomolov instab…
Sums of Squares: A Real Projective Story
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
The relationship between nonnegative polynomials and sums of squares is one of the central questions in real algebraic geometry. A modern approach is to look at nonnegative polynom…