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SUMMARY:Yifeng Huang (University of Michigan)
DTSTART:20201106T170000Z
DTEND:20201106T180000Z
DTSTAMP:20260423T041611Z
UID:UBC-AG/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UBC-AG/7/">C
 ohomology of configuration spaces of punctured varieties</a>\nby Yifeng Hu
 ang (University of Michigan) as part of UBC Vancouver Algebraic Geometry S
 eminar\n\n\nAbstract\nGiven a smooth complex variety $X$ (not necessarily 
 compact)\, consider the unordered configuration space $Conf^n(X)$ defined 
 as ${(x_1\,...\,x_n)\\in X^n: x_i \\neq x_j\\ \\text{for}\\ i\\neq j} / S_
 n$. The singular cohomology of $Conf^n(X)$ has long been an active area of
  research. In this talk\, we investigate the following phenomenon: "punctu
 ring once more" seems to have a very predictable effect on the cohomology 
 of configuration spaces when the variety we start with is noncompact. In s
 pecific\, a formula of Napolitano determines the Betti numbers of $Conf^n(
 X - {P})$ from the Betti numbers of $Conf^m(X)$ $(m \\leq n)$ if $X$ is a 
 smooth *noncompact* algebraic curve and $P$ is a point. We present a new p
 roof using an explicit algebraic method\, which also upgrades this formula
  about Betti numbers into a formula about mixed Hodge numbers and generali
 zes this formula to certain cases where $X$ is of higher dimension.\n
LOCATION:https://researchseminars.org/talk/UBC-AG/7/
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