Seminar

Commutative Algebra and Algebraic Geometry

     Tuesdays, 3:45-6pm in Evans 939

       organizer: David Eisenbud

       http://hosted.msri.org/alg  

Date: Nov 25

3:45 Bernd Sturmfels: The Hurwitz Form of a Projective Variety

The Hurwitz form of a variety is the discriminant that characterizes linear spaces of complementary dimension which intersect the variety in fewer than degree many points. We study computational aspects of the Hurwitz form, relate this to the dual variety and Chow form, and show why reduced degenerations are special on the Hurwitz polytope.

5:00 Winfried Bruns: Maximal minors and linear powers

Abstract: We say that an ideal I in a polynomial ring S has linear powers if all the powers of I have a linear free resolution. We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers. The required genericity is expressed in terms of the heights of the ideals of lower order minors. In particular we prove that all ideals defining rational normal scroll have linear powers. (This is joint work with Aldo Conca and Matteo Varbarao, to appear in J. Reine Angew. Math.)