Seminari del Dipartimento



Counting maps with prescribed incidence conditions Integral Chow ring of moduli of stable 1-pointed curves of genus two

Gavril Farkas (Humboldt) e Andrea di Lorenzo (Humboldt)

10-03-2022 - 14:00
Largo San Leonardo Murialdo,1 - Pal.C


Farkas: Counting maps with prescribed incidence conditions.

Abstract: The question of computing the number of maps of fixed degree d 
from a curve to a target variety X and verifying n incidence conditions 
can be viewed as a counterpart of the problem of determining the 
Gromov-Witten invariants of X. Using degeneration and Schubert calculus, 
we solve this problem when the target variety is the projective space of 
dimension r, and determine these numbers completely for linear series of 
arbitrary dimension when d is sufficiently large, and for all d when 
either r=1 or n=r+2. Our formulas generalize and give new proofs of very 
recent results of Tevelev and of Cela-Pandharipande-Schmitt. Joint work 
with Carl Lian.

Di Lorenzo: Integral Chow ring of moduli of stable 1-pointed curves of genus two
Abstract: Moduli of curves play a prominent role in algebraic geometry. In particular, their rational Chow rings have been the subject of intensive research in the last forty years, since Mumford first investigated the subject.
There is also a well defined notion of integral Chow ring for these objects: this is more refined, but also much harder to compute. In this talk I will present the computation of the integral Chow ring of moduli of stable 1-pointed curves of genus two, obtained by using a new approach to this type of questions (joint work with Michele Pernice and Angelo Vistoli).

Il seminario sarà presentato in presenza nell'aula M3. Tutti gli afferenti all'università Roma Tre potranno accedere previa esibizione del greenpass. Gli esterni che fossero interessati a partecipare possono contattare gli organizzatori all'email

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