INTRODUCTION TO GROMOV-WITTEN INVARIANTS
Barbara Fantechi (Università di Trento) and Lothar Göttsche (ICTP)
The course aims at introducing the fundamental notions
related to the Gromov-Witten theory.
It will include an introduction to the
language of schemes.
PRELIMINARY PROGRAMME
- Schemes of finite type over a field: definition,
morphisms, main properties.
- Functor of points associated to a scheme and introduction to the moduli
problem.
- Infinitesimal study of schemes and elements of deformation theory.
- Moduli spaces of (pointed) curves and their compactifications.
- Moduli of stable maps.
-
Construction of a fine moduli stack.
- Gromov-Witten invariants for smooth
projective varieties.
- Quantum cohomology.
BASIC REFERENCES
Hartshorne, Algebraic Geometry.
Eisenbud - Harris, Schemes, the language of modern algebraic geometry.
Aluffi, Mittag-Leffler Notes on Quantum Cohomology.
SCHEDULE
The course will consist in about 20 two-hour lectures and will start on
Tuesday, February 2nd, 1999.
The lectures will normally take place
in Room D (Basement, SISSA Main Building).
For the schedule please refer to this URL