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SUMMARY:Tautological projection of the Prym cycle
DTSTART:20260521T083000Z
DTEND:20260521T093000Z
DTSTAMP:20260813T235200Z
UID:indico-event-15392@indico.math.cnrs.fr
DESCRIPTION:Speakers: Navid Nabijou (Queen Mary University of London.)\n\n
 The moduli space of abelian varieties admits a tautological ring generated
  by lambda classes. In contrast to the space of stable curves\, this tauto
 logical ring has a remarkably simple presentation. This allows for the con
 struction of a canonical “tautological projection” which maps the full
  Chow ring onto the tautological subring. Given a Chow class on the moduli
  space of abelian varieties\, it is natural to try to compute its tautolog
 ical projection. For the locus of Jacobians\, an algorithm was provided by
  Faber.\nWe establish a corresponding algorithm for the locus of Prym vari
 eties associated to G-covers\, for G a finite group. The novel geometric c
 ontent is a closed formula relating three different types of lambda classe
 s on the moduli space of admissible G-covers\, along with a fundamental in
 variance property of these lambda classes.\nWe have implemented this algor
 ithm on a computer\, leading to many new closed formulae for tautological 
 projections. In the cases where the Prym cycle has codimension zero the al
 gorithm computes the degree of the Prym-Torelli morphism\, giving new inte
 rsection-theoretic proofs of results due variously to Donagi-Smith\, Nagar
 aj-Ramanan\, Bardelli-Ciliberto-Verra\, Marcucci–Naranjo\, and Lange–O
 rtega.\nThis is joint work in progress with Yoav Len and Sam Molcho. \n\n
 https://indico.math.cnrs.fr/event/15392/
URL:https://indico.math.cnrs.fr/event/15392/
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