Thu, October 24, 2019
Public Access Category: All |
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- Time:
- 11:45am-12:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Amit Kumar Singh.
Affiliation: IIT Madras.
Date and Time: Thursday 24 October, 11:45 am - 12:45 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Semi-stability of certain vector bundles on elliptic curves.
Abstract: Abstract Let L be a line bundle of degree d on an elliptic curve C and ϕ : C → P
n
is a morphism
given by a sub-linear system of the complete linear system |L| of dimension n + 1. When d = 4, n
= 2, we prove that ϕ
∗TPn is semi-stable if deg(ϕ(C)) > 1. Moreover, we prove that ϕ
∗TPn is isomorphic to direct sum of two isomorphic line bundles if and only if deg(ϕ(C)) = 2. Conversely, for any
rank two semi-stable vector bundle E on an elliptic curve C of degree 4, there is a non-degenerate
morphism ϕ :C → P
n
such that ϕ
∗TPn (−1) = E. More precisely, E is isomorphic to direct sum of two
isomorphic line bundles if and only if deg(ϕ(C)) = 2. Further E is either indecomposable or direct
sum of non-isomorphic line bundles if and only if deg(ϕ(C)) = 4. When d = 5, n = 3, we compute
the Harder-Narasimhan filtration of ϕ
∗TPn .
- Time:
- 3:30pm-5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra seminar II.
Speaker: Tony Puthenpurakal.
Affiliation: IIT Bombay.
Date and Time: Thursday 24 October, 3:30 pm - 5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Triangulated categories-I,II,III.
Abstract: We define and give elementary properties of triangulated
categories. We also give an application of triangulated categories to
linkage theory in commutative algebra.