BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Sam Molcho (ETH)
DTSTART:20210409T190000Z
DTEND:20210409T200000Z
DTSTAMP:20260407T230913Z
UID:agstanford/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/4
 6/">The strict transform in logarithmic geometry</a>\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/
END:VEVENT
END:VCALENDAR