M.I.T. Algebraic Geometry Seminar - Andreas Gathmann
Friday April 9, 4:00pm-5:30pm
Room 2-255
Computing Gromov-Witten invariants of quintic threefolds via
degeneration techniques
We give a new geometric method to compute the genus zero Gromov-Witten
invariants of quintic threefolds in P^4, reproving the formula
conjectured by the physicists Candelas et al. in 1991. The idea is to
look at irreducible degree-d curves in P^4 having multiplicity k to
the quintic at some point of the curve. By degeneration techniques, we
can describe explicitly how to solve enumerative problems for these
curves in terms of others with smaller d or k. This allows one finally
to compute recursively the case k = 5d+1 for all d, corresponding to
degree-d curves in the quintic.
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