Fri, March 30, 2018
Public Access Category: All |
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- Time:
- 4:00pm
- Location:
- Room No. 216, Department of Mathematics
- Description:
- Student Seminar
Title: An example which motivates why we need line bundles.
Speaker: Soumyadip Thandar
Abstract: This will be a motivational seminar about the importance of line
bundles( ie, vector bundles of rank 1). Giving a vector bundle of rank k
over some space is equivalent to give some data, such as an open cover for
the space, and a collection of maps from the intersections of these open
sets to Gl(k,C). We will first construct CP^n by gluing (n+1) copies of
C^n. We will then construct a special line bundle, called O(1), over CP^n ,
which possesses global sections. The main goal will be to prove that giving
a morphism from X to CP^n is equivalent to give a line bundle over X and
(n+1) sections which do not vanish simultaneously.
Time and Venue: Friday, 30th March, 4pm, Room 216