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33 papers · 1 filter
A rigid irregular connection on the projective line
Edward Frenkel, Benedict Gross
In this paper we construct a connection on the trivial G-bundle on the projective line for any simple complex algebraic group G, which is regular outside of the points 0 and infini…
The Hilbert scheme of the diagonal in a product of projective spaces
Dustin Cartwright, Bernd Sturmfels
The diagonal in a product of projective spaces is cut out by the ideal of 2x2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has…
Polynomial relations among principal minors of a 4x4-matrix
Shaowei Lin, Bernd Sturmfels
The image of the principal minor map for n x n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations amo…
Powers of Ideals and Fibers of Morphisms
David Eisenbud, Joe Harris
Let X\subset PP^n be a projective scheme over a field, and let phi:X --> Y be a finite morphism. Our main result is a formula in terms of global data for the maximum of the Casteln…
On the equations for universal torsors over del Pezzo surfaces
Vera Serganova, Alexei Skorobogatov
We show that every split del Pezzo surface of degree d=5,4,3 or 2 has a universal torsor which is a dense open subset of the intersection of 6-d dilatations of the affine cone over…
Sagbi Bases of Cox-Nagata Rings
Bernd Sturmfels, Zhiqiang Xu
We degenerate Cox-Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration impli…