Séminaires : Séminaire de géométrie algébrique

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Email des responsables : frederic.han@imj-prg.fr
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Le jeudi à 14h.
septembre-décembre Sophie-Germain, janvier-mars ENS, avril-juin Jussieu

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Orateur(s) Gavril Farkas - ,
Titre Counting maps with prescribed incidence conditions.
Horaire14:00 à 15:00
RésumeZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion
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 Hurwitz numbers. 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.