CACAAG (Combinatorial Aspects of Commutative Algebra and Algebraic
Geometry) seminar
Speaker: Ronnie Sebastian
Date & Time : 19th February, 3:30pm
Venue : Ramanujan Hall
Abstract: This talk will be based on the following elementary and nice
exposition
http://www.math.stonybrook.edu/~roblaz/Reprints/Green.
Laz.Simple.Pf.Petri.pdf
Using some simple facts about projective space, cohomology, cohomology of
line bundles on projective space, we shall prove the following theorems:
1. Noether's theorem - Projective normality of the canonical embedding of
non-hyperelliptic curves.
2. Petri's -theorem - Let X be a smooth and projective curve of genus g
\geq 5. Assume that X carries a line bundle A of degree g-1 with h^0(A)=2.
Further assume that both A and \Omega_X\otimes A^* are generated by their
global sections. Then the homogeneous ideal of X in its canonical embedding
is generated by degree 2 elements.