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SUMMARY:Sam Molcho (ETH)
DTSTART;VALUE=DATE-TIME:20210409T190000Z
DTEND;VALUE=DATE-TIME:20210409T200000Z
DTSTAMP;VALUE=DATE-TIME:20221209T123456Z
UID:agstanford/46
DESCRIPTION:Title: The strict transform in logarithmic geometry\nby Sam Molcho (ETH)
as part of Stanford algebraic geometry seminar\n\n\nAbstract\nLet $(X\,D)$
be a pair of a smooth variety and a normal crossings divisor. The loci of
curves that admit a map to X with prescribed tangency along D exhibit som
e pathological behavior: for instance\, the locus of maps to a product $(X
\\times Y\, D \\times E)$ does not coincide with the intersection of the
loci of maps to $(X\,D)$ and $(Y\,E)$. In this talk I want to explain how
the root of such pathologies arises from the difference between taking the
strict and total of a cycle under a very special kind of birational map\,
called a logarithmic modification. I will discuss how for a logarithmic m
odification\, the strict transform of a cycle has a modular interpretation
\, and how its difference with the total transform can be explicitly compu
ted\, in terms of certain piecewise polynomial functions on a combinatoria
l shadow of the original spaces\, the tropicalization. Time permitting\, I
will discuss some applications -- for instance\, how these calculations i
mply that loci of curves with a map to a toric variety lie in the tautolog
ical ring.\n
LOCATION:https://researchseminars.org/talk/agstanford/46/
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