Student Commutative Algebra Seminar

Let C be a curve in the 3-dimensional projective space P^3. Hartshorne's conjecture says that as long as it is irreducible, the curve C can be defined using only two equations. While easy to state, this conjecture has not been resolved. We study this conjecture using local cohomology, which is was originally constructed in the 1960s as a tool to study sheaves and their cohomology in algebraic geometry. Since then, it has become a powerful tool in commutative algebra, especially because local cohomology is very computable. In this talk, we will focus on examples and computations concerning Hartshorne's conjecture, and will only assume knowledge from MATH 593 for the majority of the talk. Speaker(s): Takumi Murayama (University of Michigan)