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SUMMARY:Hannah Larson (Berkeley\, Clay Mathematical Institute)
DTSTART:20240524T193000Z
DTEND:20240524T203000Z
DTSTAMP:20260406T162727Z
UID:agstanford/136
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 36/">The Chow ring of the universal Picard stack over the hyperelliptic lo
 cus</a>\nby Hannah Larson (Berkeley\, Clay Mathematical Institute) as part
  of Stanford algebraic geometry seminar\n\nLecture held in 383-N.\n\nAbstr
 act\nI'll start by defining the Chow ring\, which is an important invarian
 t of a scheme (or stack). Next\, I will define the Picard variety and Pica
 rd stack of a curve\, and then introduce their universal versions $J^d_g$ 
 and $\\mathscr{J}^d_g$ over the moduli space of curves $M_g$. Recently\, p
 rogress has been made studying the Chow ring of $M_g$ in low genus by stra
 tifying the moduli space by gonality (the minimal degree of a map to $\\ma
 thbb{P}^1$). The smallest piece in this stratification is the hyperellipti
 c locus. Motivated by this\, I'll present several results about the restri
 ction of $\\mathscr{J}^d_g$ to the hyperelliptic locus\, denoted $\\mathsc
 r{J}^d_{2\,g}$. These include a presentation of the rational Chow ring of 
 $\\mathscr{J}^d_{2\,g}$. I also determine the integral Picard group of $\\
 mathscr{J}^d_{2\,g}$\, completing (and extending to the $PGL_2$-equivarian
 t case) prior work of Erman and Wood.\n\nNotice unusual time so Eleny Ione
 l can attend!\n
LOCATION:https://researchseminars.org/talk/agstanford/136/
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