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SUMMARY:Renzo Cavalieri (Colorado State University)
DTSTART;VALUE=DATE-TIME:20211119T200000Z
DTEND;VALUE=DATE-TIME:20211119T210000Z
DTSTAMP;VALUE=DATE-TIME:20221209T120732Z
UID:agstanford/69
DESCRIPTION:Title: The integral Chow ring of $M_{0}(\\mathbb{P}^r\,d)$\nby Renzo Cava
lieri (Colorado State University) as part of Stanford algebraic geometry s
eminar\n\n\nAbstract\nWe give an efficient presentation of the Chow ring w
ith integral coefficients of the open part of the moduli space of rational
maps of odd degree to projective space. A less fancy description of this
space has its closed points correspond to equivalence classes of $(r+1)$-t
uples of degree $d$ polynomials in one variable with no common positive de
gree factor. We identify this space as a $GL(2\,\\mathbb{C})$ quotient of
an open set in a projective space\, and then obtain a (highly redundant) p
resentation by considering an envelope of the complement. A combinatorial
analysis then leads us to eliminating a large number of relations\, and to
express the remaining ones in generating function form for all dimensions
. The upshot of this work is to observe the rich combinatorial structure c
ontained in the Chow rings of these moduli spaces as the degree and the ta
rget dimension vary. This is joint work with Damiano Fulghesu.\n\nThe sync
hronous discussion for Renzo Cavalieri’s talk is taking place not in zoo
m-chat\, but at https://tinyurl.com/2021-11-19-rc (and will be deleted aft
er ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/69/
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