102 citations · 200 across the 13 of their papers we have counts for
4 papers · 1 filter
The Graph of Monomial Ideals
Klaus Altmann, Bernd Sturmfels
There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring. The definition involves Gröbner bases or the action of an algebraic torus. We present…
Higher Lawrence configurations
Francisco Santos, Bernd Sturmfels
Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove…
Toric Hyperkahler Varieties
Tamas Hausel, Bernd Sturmfels
Extending work of Bielawski-Dancer and Konno, we develop a theory of toric hyperkahler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework…
Multigraded Hilbert Schemes
Mark Haiman, Bernd Sturmfels
We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our con…