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Scrollar invariants, resolvents, and syzygies

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Scrollar invariants, resolvents, and syzygies

With every cover C -> P^1 of the projective line one can associate its so-called scrollar invariants (also called Maroni invariants) which describe how the push-forward of the structure sheaf of C splits over P^1. They can be viewed as geometric counterparts of the successive minima of the lattice associated with the ring of integers of a number field. In this talk we consider the following problem: how do the scrollar invariants of the Galois closure C’ -> P^1 and of its various subcovers (the so-called resolvents of C -> P^1) relate to known invariants of the given cover? This concerns ongoing work with Yongqiang Zhao, in which we put a previous observation for covers of degree 4 due to Casnati in a more general framework. As we will see the answer involves invariants related to syzygies that were introduced by Schreyer. As time permits, we will discuss a number-theoretic manifestation of the phenomena observed.

- Séminaire Géométrie et théorie des modèles

Détails :

Orateur / Oratrice : Wouter Castryck
Date : 11 janvier 2019
Horaire : 11h00 - 12h30
Lieu : ENS Salle W