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Renzo Cavalieri |
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T-Th 10 – 11:30 am |
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East Hall 3096 |
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Any
relevant information about this course will (hopefully) appear on this webpage.
This course is meant to be a “soft” and intuitive introduction to Gromov-Witten theory, the study of intersection theory on moduli spaces of stable maps. It would be unfair (and incorrect) to
claim that this is a particular area of algebraic geometry. Rather, it is an
area of mathematics that involves algebraic geometry, but really finds its
roots in mathematical physics and goes to touch, according to your flavor,
analysis, topology, symplectic geometry, combinatorics etc
The
presentation of the subject is hopefully going to be (whether fully honestly or
not we’ll have to see…) deprived of its most technical
aspects and the point of view of a “generic geometer” will be
adopted – so the class can be useful, interesting and accessible also to
graduate students in neighboring areas.
References (the list
will grow as the class unravels):
1. An
invitation to Quantum Cohomology. Kontsevich's
formula for rational plane curves.
This beautiful and reasonably elementary book
by Kock and Vainsencher is
an excellent introduction to GW theory, from the point of view of someone
particularly interested in enumerative geometry. It will be accompanying us for
the first month or so of class.
2. Notes on stable maps and quantum cohomology.
A classic. Fulton and Pandharipande’s
lecture notes. More general, more technical.
Another beautiful expository work of Joachim Kock. All the ins and outs of gravitational descendants
unveiled here.
1.
Sean Keel's paper describing the Chow ring of these spaces.
2.
On the projectivity of the moduli space of Stable Curves (I),
Knudsen's original papers on \bar{M}_{0,n}.
Fantechi's friendly expose' .
A slightly more detailed while still clear introducion.
1.
Behrend "as friendly as it gets" article on GW invariants and the virtual fundamental class.
2.
Graber-Pandharipande bring localization into high genus GW theory.