UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 03, 2017

939 Evans Hall

3:45PM: Algebraic Aspects of Lattice Polytopes

Benjamin Braun

To a lattice polytope P one can associate a graded semigroup algebra K[P]. A well-known theorem due to Hochster implies that K[P] is Cohen-Macaulay, and since the 1970's there has been a fruitful interaction between combinatorics and commutative algebra using this construction. In this talk I will discuss (1) several open problems regarding the Hilbert series of K[P] (often referred to as the Ehrhart series of P) and (2) recent joint work with my student Brian Davis regarding free resolutions of K over K[P] and rationality of the associated Poincare series for a specific family of lattice polytopes.

5:00PM: Liaison among curves in P^3

Mengyuan Zhang

Two curves X and Y are linked if their union is a complete intersection in P3. The equivalence relation generated by linkage is called liaison. We survey the results on free resolution of curves, classification of liaison classes and minimal curves, and mention the relevance to the study of the Hilbert scheme of curves in P^3.

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