Fri, October 26, 2018
Public Access


Category:
Category: All

26
October 2018
Mon Tue Wed Thu Fri Sat Sun
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31        
8:00am  
9:00am  
10:00am  
11:00am  
12:00pm  
1:00pm  
2:00pm  
3:00pm  
4:00pm [4:00pm] Soumyadip Thandar
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).

5:00pm  
6:00pm