INTRODUCTION TO GROMOVWITTEN INVARIANTS
Barbara Fantechi (Università di Trento) and Lothar Göttsche (ICTP)
The course aims at introducing the fundamental notions
related to the GromovWitten 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.
 GromovWitten invariants for smooth
projective varieties.
 Quantum cohomology.
BASIC REFERENCES
Hartshorne, Algebraic Geometry.
Eisenbud  Harris, Schemes, the language of modern algebraic geometry.
Aluffi, MittagLeffler Notes on Quantum Cohomology.
SCHEDULE
The course will consist in about 20 twohour 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