173 citations · 472 across the 28 of their papers we have counts for
21 papers · 1 filter
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…
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…
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…
Smooth Hilbert schemes: their classification and geometry
Roy Skjelnes, Gregory G. Smith
Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polyn…
Sums of Squares and Quadratic Persistence on Real Projective Varieties
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
We bound the Pythagoras number of a real projective subvariety: the smallest positive integer such that every sum of squares of linear forms in its homogeneous coordinate ring…