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Ronnie Sebastian

Description: CACAAG (Combinatorial Aspects of Commutative Algebra and Algebraic
Geometry) seminar

Speaker: Ronnie Sebastian

Date & Time : 26th February, 2pm

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.
Location: Ramanujan Hall, Department of Mathematics
Date: Monday, February 26, 2018
Time: 2:00pm IST
Access: Public