Divisor Theory on Curves

Student Algebraic Geometry Seminar
Friday, October 13, 2017 - 10:00
1 hour (actually 50 minutes)
Skiles 114
GA Tech
We will give an overview of divisor theory on curves and give definitions of the Picard group and the Jacobian of a compact Riemann surface.  We will use these notions to prove Plucker’s formula for the genus of a smooth projective curve.  In addition, we will discuss the various ways of defining the Jacobian of a curve and why these definitions are equivalent.  We will also give an extension of these notions to schemes, in which we define the Picard group of a scheme in terms of the group of invertible sheaves and in terms of sheaf cohomology.