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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. |

Location: | Ramanujan Hall, Department of Mathematics |

Date: | Monday, February 19, 2018 |

Time: | 3:30pm IST |

Access: | Public |