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SUMMARY:Massimo Bagnarol (SISSA): On the cohomology of moduli spaces of st
able maps to Grassmannians
DTSTART;VALUE=DATE-TIME:20190913T120000Z
DTEND;VALUE=DATE-TIME:20190913T130000Z
DTSTAMP;VALUE=DATE-TIME:20201205T084342Z
UID:indico-event-4818@indico.math.cnrs.fr
DESCRIPTION:Being the basis of Gromov-Witten theory\, Kontsevich's moduli
spaces of stable maps are important in different areas of mathematics and
theoretical physics. For this reason\, it is interesting to study their ge
ometry\, for example analyzing their (co)homology. In fact\, determining t
heir Betti/Hodge numbers is already a nontrivial problem. In this talk\, I
will present a method for computing the Betti/Hodge numbers of moduli spa
ces of stable maps from genus 0 curves to a Grassmann variety G(r\,V). Fir
st\, by using the combinatorial properties of these spaces\, I will show t
hat the problem can be reduced to the computation of the Hodge numbers of
the open locus parametrizing stable maps from smooth curves. Then\, I will
show how the latter can be explicitly calculated\, by means of a suitable
Quot scheme compactification of the space of morphism of fixed degree fro
m the projective line to G(r\,V).\n\nhttps://indico.math.cnrs.fr/event/481
8/
LOCATION:batiment I 001
URL:https://indico.math.cnrs.fr/event/4818/
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