Description

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.

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.

Description

Ramanujan Hall, Department of Mathematics

Date

Mon, February 19, 2018

Start Time

3:30pm IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Mon, February 19, 2018 2:19am IST