Gergely Bérczi: Katalogdaten im Frühjahrssemester 2017

NameHerr Dr. Gergely Bérczi
DepartementMathematik
BeziehungDozent

NummerTitelECTSUmfangDozierende
401-4148-17LReading Course: Introduction to the Moduli of Maps and Gromow-Witten Invariants2 KP4AG. Bérczi
KurzbeschreibungEnumerative questions motivated the development of algebraic geometry for centuries. This course is a short tour to some ideas which have revolutionised enumerative geometry in the last 30 years: stable maps, Gromov-Witten invariants and quantum cohomology.
LernzielThe aim of the course is to understand the concept of stable maps, their moduli and quantum cohomology. We prove Kontsevich's celebrated formula on the number of plane rational curves of degree d passing through 3d-1 given points in general position.
InhaltTopics covered:
1) Brief survey on moduli spaces: fine and coarse moduli.
2) Stable n-pointed curves
3) Stable maps
4) Enumerative geometry via stable maps
5) Gromov-Witten invariants
6) Quantum cohomology and quantum product
7) Kontsevich's formula
LiteraturThe main reference for the course is:
J. Kock and I.Vainsencher: Kontsevich's Formula for Rational Plane Curves
www.math.utah.edu/%7eyplee/teaching/gw/Koch.pdf

Background material:
-Algebraic varieties: I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
-Moduli of curves: Joe Harris and Ian Morrison, Moduli of Curves, Graduate Texts in Mathematics 187, Springer-Verlag
-Moduli spaces (fine and coarse): Peter. E. Newstead, Introduction to Moduli Problems and Orbit Spaces, Tata Institute Lecture Notes, Springer-Verlag
Voraussetzungen / BesonderesSome minimal background in algebraic geometry (varieties, line bundles, Grassmannians, curves).
Basic concepts of moduli spaces (fine and coarse) and group actions will be explained mainly through examples.