Fri, October 26, 2018
Public Access Category: All |
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- Time:
- 4:00pm
- Location:
- Room No. 215, Department of Mathematics
- Description:
- Speaker: Soumyadip Thandar
Time and Venue: 4pm, room 215
Title: General position theorem
Abstract: Let X be a smooth projective variety contained in CP^n. We say X is nondegenerate if it is not contained in any proper hyperplane. Given a variety of dimension m in CP^n, we intersect it with m many hyperplanes and get bunch of points. This number is independent of the choice of the hyperplanes and is defined to be the degree of the variety. A set of k points in CP^n is said to be in general position, if every subset of n+1 points spans all of CP^n. We will prove the general position theorem which states that given an irreducible nondegenerate curve C in CP^n ( where n is \geq 3) of degree d, a general hyperplane meets C in d points which are in general position. Using this we will show any nondegenerate variety X in CP^n , degree \geq 1+codim(X).