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SUMMARY:Yilong Zhang (Ohio State University)
DTSTART:20201130T210000Z
DTEND:20201130T220000Z
DTSTAMP:20260423T035915Z
UID:AGSAGS/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGSAGS/14/">
 Cubic Threefolds and Vanishing Cycles on its Hyperplane sections</a>\nby Y
 ilong Zhang (Ohio State University) as part of American Graduate Student A
 lgebraic Geometry Seminar\n\n\nAbstract\nFor a general cubic threefold\, a
  vanishing cycle on a smooth hyperplane section is an integral 2-class per
 pendicular to the hyperplane class with self-intersection equal to -2. The
  question is what is a vanishing cycle on a singular hyperplane section? W
 e will show that there is a certain moduli space parameterizing "vanishing
  cycles" on all hyperplane sections and the boundary divisor answers the q
 uestion. As a vanishing cycle on a smooth cubic surface is represented by 
 the difference of two skew lines\, such moduli space arises as a quotient 
 of the Hilbert scheme of skew lines on the cubic threefold. Based on the A
 bel-Jacobi map on cubic threefolds studied by Clemens and Griffiths\, we'l
 l show that the moduli space is isomorphic to the blowup of the theta divi
 sor of the at an isolated singularity.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/14/
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