Séminaire géométrie complexe

L’exposé aura lieu à 13h45 au lieu de 14h car la salle Döblin est réservée à 15h pour un pot de thèse.

Mihai PAVEL (Bucarest)

Titre : Projectivity of moduli of higher-rank PT-stable pairs on threefolds

Résumé : Stable pairs were introduced by Pandharipande and Thomas to define new curve-counting invariants on Calabi–Yau threefolds. It was soon observed (independently by Bayer and Toda) that such objects can be understood via a generalized notion of stability on the derived category of coherent sheaves. This notion, known as Pandharipande–Thomas (PT) stability, extends the original construction and recovers the stable pairs of Pandharipande and Thomas as PT-stable objects of rank 1 and trivial determinant. One is naturally led to study the moduli theory of PT-stable objects on projective threefolds. However, unlike the original case, the moduli problem for higher-rank PT-stable objects is not known to be associated with a GIT problem, and hence it is unknown whether the moduli spaces are projective. In this talk, we present recent progress on this problem, based on joint work with Tuomas Tajakka.