101 citations · 245 across the 21 of their papers we have counts for
7 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…
Calabi-Yau threefolds in and Gorenstein rings
Hal Schenck, Mike Stillman, Beihui Yuan
A projectively normal Calabi-Yau threefold has an ideal which is arithmetically Gorenstein, of Castelnuovo-Mumford regularity four. Such ideals hav…
Computations in intersection rings of flag bundles
Daniel R. Grayson, Alexandra Seceleanu, Michael E. Stillman
Intersection rings of flag varieties and of isotropic flag varieties are generated by Chern classes of the tautological bundles modulo the relations coming from multiplicativity of…
High rank linear syzygies on low rank quadrics
Hal Schenck, Mike Stillman
We study the linear syzygies of a homogeneous ideal I in a polynomial ring S, focusing on the graded betti numbers b_(i,i+1) = dim_k Tor_i(S/I, k)_(i+1). For a variety X and diviso…
Algebraic Geometry of Bayesian Networks
Luis David Garcia, Michael Stillman, Bernd Sturmfels
We study the algebraic varieties defined by the conditional independence statements of Bayesian Networks. A complete algebraic classification is given for Bayesian Networks on at m…
Algorithms for the Toric Hilbert Scheme
Michael Stillman, Bernd Sturmfels, Rekha R. Thomas
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among…