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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Curve counting on surfaces - Martijn Kool (Imperia
l College)
DTSTART;TZID=Europe/London:20121121T141500
DTEND;TZID=Europe/London:20121121T151500
UID:TALK41177AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/41177
DESCRIPTION:Counting nodal curves in (sufficiently ample) line
ar systems |L| on smooth projective surfaces S is
a problem with a long history. The Göttsche conjec
ture\, now proved by several people\, states that
these counts are universal and only depend on c_1(
L)^2\, c_1(L)⋅c_1(S)\,\nc_1(S)^2 and c_2(S). We li
nk this classical curve count to certain Gromov-Wi
tten and stable pair invariants (with many point i
nsertions) on S. This can be see as version of the
MNOP conjecture for the canonical bundle K_S. Dro
pping the ``sufficiently ample'' condition on\nL\,
we show stable pair invariants of S can still be
computed and are also universal and topological. T
his is joint work with R. P. Thomas.
LOCATION:MR 13\, CMS
CONTACT:Caucher Birkar
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