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Kempner Colloquium
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\begin{Huge}\textsc{Counting curves virtually}
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\begin{Large}\textbf{Jonathan Wise}
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Stanford University
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\begin{quote}
The collection of algebraic curves in a projective complex variety can
be completed to a moduli space in many different ways.  When the
number of equations of such a moduli space matches the number of
variables, one expects the moduli space to be a finite collection of
points.  In practice, however, redundancies among the equations lead
to moduli spaces of high dimension with bad singularities.

Nevertheless, it is often possible to define a ``virtual" number of
points for these unexpectedly complicated moduli spaces.  In this
talk, I will explain how virtual enumeration works in a very familiar
example and then describe several different ways of applying these
ideas to the enumeration of curves in a smooth projective variety with
prescribed tangency conditions along a smooth divisor.  Finally, I
will explain how these different approaches are related.
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January 27, 2012

3:00 p.m.

MATH 350

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