Intensive Course on Intersection Theory


Dates: July 26-28, 2016
Venue: JGU Mainz, Hilbertraum

Abolfazl Mohajer
Ariyan Javanpeykar
Carsten Liese
Davide Veniani
Helge Ruddat
Peter Overholser
Robert Wilms
Simon Felten
Timo Riske
Tom Sutherland

Goal and material:
A goal is that after this course each of us is familiar with intersection theory as covered by Fulton's book (reference a). We want to know what is dealt with in the book and what the mathematical tools presented are useful for and how they work and interact, so that whenever needed in the future, details can be looked up quickly. The focus of our course is on the big picture and crucial corner stones, on breadth and road map rather than depth and detail.


Tu, Jul 26 We, Jul 27 Th, Jul 28
9:00-10:00 (1) Ruddat (6) Overholser (11) Overholser
10:30-11:30 (2) Felten (7) Sutherland (12) Wilms
12:00-13:00 (3) Veniani (8) Riske (13) Sutherland
14:30-15:30 (4) Mohajer (9) Ruddat (14) Veniani
16:00-17:00 (5) Liese (10) Javanpeykar


Page numbers refer to reference (a) and lecture numbers refer to reference (b):
(1) Introduction, Rational Equivalence, Divisors, Vector Bundles and Chern Classes pp. 1-69, Lectures 1-11
(2) Cones and Segre Classes, Deformation to the Normal Cone pp. 70-91, Lectures 12-15
(3) Intersection Products pp. 92-118, Lecture 16
(4) Intersection Multiplicities, Intersections on Non-singular Varieties pp. 119-152
(5) Excess and Residual Intersections pp. 153-175, Lecture 17
(6) Families of Algebraic Cycles pp. 175-194
(7) Dynamic Intersections pp. 195-209
(8) Positivity, Rationality pp. 210-241
(9) Degeneracy Loci and Grassmannians pp. 242-279
(10) Riemann-Roch for Non-singular Varieties pp. 280-304, Lectures 18-19
(11) Correspondences, Bivariant Intersection Theory pp. 305-338, Lectures 20-21
(12) Riemann Roch for Singular Varieties pp. 339-369
(13) Algebraic, Homological and Numerical Equivalence pp. 370-392
(14) Generalizations pp. 393-405

(a) William Fulton: "Intersection Theory", 2nd Edition, Springer
(b) Ravi Vakil's lecture notes