NCMW - Intersection Theory (2022)
Speakers and Syllabus
Speakers and Syllabus:
Name of the Speakers with their affiliation. |
No. of Lectures |
Detailed Syllabus |
Nitin Nitsure (NN) |
6 |
Basics of intersection theory (Cycles, rational equivalence, functoriality properties, relevant commutative algebra background) Main reference: Fulton, Chapter 1 |
Amit Hogadi (AH) |
4 |
Vector bundles and Chern classes (Divisors and line bundles, intersection with divisors, Gysin map for divisors, Segre classes, Chern classes, the projective bundle formula) Main reference: Fulton chapters 2, 3 |
Chetan Balwe (CB) |
4 |
Deformation to the normal cone (Segre class of a cone, Segre class of a subscheme, multiplicity along a subvariety, deformation to the normal cone) Main reference: Fulton chapters 4, 5 |
Anand Sawant (AS) |
4 |
The intersection product (Construction of the intersection product using reduction to the diagonal, the moving lemma and Serre’s Tor formula) Main reference: Fulton chapters 6, 11 |
V. Srinivas (VS) |
6 |
The Grothendieck Riemann-Roch theorem (The Chern character, Todd classes, the Grothendieck group of veector bundles, the Grothendieck Riemann-Roch theorem) |
Kapil Paranjape (KP) |
4 |
Overview of connections of intersection theory with Hodge theory |
Time Table
Tentative time-table, mentioning names of the speakers and tutors with their affiliation:
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.–11.30) |
Lecture 2 (11.30–1.00) |
Lunch (1.00–2.30) |
Lecture 3 (2.30–4.00) |
Tea /Snacks (4.00-4.30) |
Lecture 4/Discussion (4.30-5.30) |
|
|
(Name of the speaker) |
|
(Name of the speaker) |
|
(Name of the speaker) |
|
(Name of the speaker) |
Mon |
02/05 |
NN 1 |
|
AH 1 |
|
NN 2 |
|
Discussion |
Tues |
03/05 |
NN 3 |
|
AH 2 |
|
CB 1 |
|
Discussion |
Wed |
04/05 |
NN 4 |
|
AH 3 |
|
Discussion |
|
--- |
Thu |
05/05 |
NN 5 |
|
AH 4 |
|
CB 2 |
|
Discussion |
Fri |
06/05 |
NN 6 |
|
CB 3 |
|
CB 4 |
|
Discussion |
Sat |
|
|
|
|
|
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|
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Sun |
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Mon |
09/05 |
AS 1 |
|
AS 2 |
|
VS 1 |
|
Discussion |
Tues |
10/05 |
AS 3 |
|
KP 1 |
|
VS 2 |
|
Discussion |
Wed |
11/05 |
AS 4 |
|
KP 2 |
|
VS 3 |
|
--- |
Thu |
12/05 |
KP 3 |
|
VS 4 |
|
VS 5 |
|
Discussion |
Fri |
13/05 |
KP 4 |
|
VS 6 |
|
Discussion |
|
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