# 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 Details available here 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) Details available here 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 Sun 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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