Algebraic Geometry Seminar
Jie Wang
Ohio State
Geometry of general curves via degenerations and deformations
Abstract: A central problem in curve theory is to describe algebraic curves in a given projective space with
fixed genus and degree. One wants to know the extrinsic geometry of the curve, i.e information on
the equations defining the curve. Koszul cohomology groups in some sense carry 'everything one
wants to know' about the extrinsic geometry of curves in projective space: the number of equations
of each degree needed to define the curve, the relations between the equations, etc. In this talk, I will
present a new method using deformation theory to study Koszul cohomology of general curves. Using this
method, I will describe a way to determine number of defining equations of a general curve in some special degree
range (but for any genus).
Monday February 7, 2011 at 4:00 PM in SEO 612