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SUMMARY:Burt Totaro (UCLA)
DTSTART:20200915T160000Z
DTEND:20200915T170000Z
DTSTAMP:20260423T021452Z
UID:eAKTS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/eAKTS/8/">To
 rus actions\, Morse homology\, and the Hilbert scheme of points on affine 
 space</a>\nby Burt Totaro (UCLA) as part of electronic Algebraic K-theory 
 Seminar\n\nLecture held in 915 7106 9041.\n\nAbstract\nWe formulate a conj
 ecture on actions of the multiplicative\n       group. In short\, if the m
 ultiplicative group $\\mathbb{G}_m$\n       acts on a quasi-projective sch
 eme $U$ such that\n       $U$ is attracted as $t$ approaches $0$ in $\\mat
 hbb{G}_m$\n       to a closed subset $Y$ in $U$\, then the inclusion from 
 $Y$ to $U$ should be\n       an $\\mathbb{A}^1$-homotopy equivalence. This
  would be useful if true\,\n       since actions of the multiplicative gro
 up occur everywhere\n       in algebraic geometry. We prove several partia
 l results.\n       The proofs use an analog of Morse theory\n       for si
 ngular varieties.\n       We give an application to the Hilbert scheme of 
 points\n       on affine space $\\mathbb{A}^n$.\n
LOCATION:https://researchseminars.org/talk/eAKTS/8/
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