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SUMMARY:Summer School on Geometry of Moduli Spaces of Curves | (smr 3215)
DTSTART;VALUE=DATE-TIME:20180618T060000Z
DTEND;VALUE=DATE-TIME:20180622T200000Z
DTSTAMP;VALUE=DATE-TIME:20181211T232328Z
UID:indico-event-8319@ictp.it
DESCRIPTION:\n Moduli spaces of stable pointed curves play an important ro
le in algebraic geometry. This School will have one course on vector bundl
es of coinvariants and on conformal blocks and another one on their cohomo
logy classes in relation with those of moduli of abelian varieties. The co
homology of moduli spaces of curves and abelian varieties carries several
natural classes. We focus on the tautological classes and the cohomology c
lasses related to spaces of modular forms. The problem of determining rela
tionships between the tautological classes turns out to be particularly in
teresting. Moduli spaces of curves carry vector bundles of coinvariants an
d conformal blocks\; they are invariants of a curve C attached to a Lie gr
oup G that are canonically isomorphic to global sections of an ample line
bundle on the moduli stack of certain G-bundles on C. These are generalize
d theta functions in case C is smooth. In case g=0\, the bundles of co-inv
ariants are globally generated\, and their first Chern classes are semi-am
ple line bundles on the moduli of curves\, and shed light on its birationa
l geometry. We can also use the moduli space of curves to learn about gene
ralized theta functions.TOPICS:Cohomology classes on moduli of curves and
abelian varieties\n moduli spaces of curves and abelian varieties\n \n
properties of the moduli spaces and their compactifications\n \n natu
ral cohomology classes and their relations\n \n tautological classes an
d cohomology classes related to spaces of modular forms\n \n Vector bund
les of coinvariants and conformal blocks\n introduction to moduli spaces
of curves\n \n open problems and F-conjecture\n \n vector bundles o
f coinvariants and conformal blocks\n \n case g=0: global generation an
d semi-ample divisors\n \n any genus: nef divisors\n \n Chern classe
s of bundles of coinvariants\n \n Global sections of ample line bundles
on Bun_G(C): smooth and nodal case\n \n \nPARTICIPATION:Women are parti
cularly encouraged to apply. Should you come to Trieste with your child(re
n)\, please send an e-mail to smr3215@ictp.it to describe your family need
s and we will do our best to meet them.\n A limited number of grants are a
vailable to support the attendance of selected participants\, with priorit
y given to participants from developing countries. There is no registratio
n fee.\n To apply\, please use the link on the left side of this web page.
\n The deadline for submitting applications expired on 15 March 2018.\n\nh
ttp://indico.ictp.it/event/8319/
LOCATION:ICTP Kastler Lecture Hall (AGH)
URL:http://indico.ictp.it/event/8319/
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