In recent years, classical enumerative problems in algebraic geometry have been converted into statements in tropical geometry. This approach has had tremendous success. In view of the current pandemic, we will stay away from these popular results. Rather, we discuss two isolated cases: the 9 inflection points of plane cubics and the 28 bitangent lines of plane quartics. The tropical counts yield 3 and 7, respectively. We will see how to reconcile these results via positive characteristic. These cases naturally generalize to inflection points of plane curves of arbitrary degree and theta-characteristics of curves of general type.
The talk assumes minimal familiarity with basic concepts of algebraic geometry over the complex numbers. Positive characteristic and tropical geometry play important, but non-technical roles.
This is joint work with Marco Pacini.
L’exposé se déroulera sur Zoom et devrait durer 45 minutes environ.
Il sera retransmis en (quasi-)direct via Twitch (grace à l’aide technique considérable apportée par Fabrice Rouillier de l’Inria).
Pour revoir l’exposé de Damiano Testa.
Slides de l’exposé : pdf