UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

November 25, 2014

939 Evans Hall


3:45PM: The Hurwitz Form of a Projective Variety

Bernd Sturmfels

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.

3:45PM: The Hurwitz Form of a Projective Variety

Bernd Sturmfels

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.

5:00PM: Maximal minors and linear powers

Winfried Bruns

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 (J. Reine Angew. Math., to appear)

5:00PM: Maximal minors and linear powers

Winfried Bruns

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.)

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