Statut  Confirmé 
Série  SEMDARBOUX 
Domaines  hepth 
Date  Jeudi 18 Octobre 2012 
Heure  16:00 
Institut  LPTENS 
Salle  bibliothèque du LPTENS 
Nom de l'orateur  Sheshmani 
Prenom de l'orateur  Artan 
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Institution de l'orateur  
Titre  DonaldsonThomas invariants of torsion 2 dimensional sheaves and modular forms 
Résumé  We study the DonaldsonThomas invariants of the 2dimensional stable sheaves in a smooth projective threefold. The DT invariants are defined via integrating over the virtual fundamental class when it exists. When the threefold is a K3 surface fibration we express the DT invariants of sheaves supported on the fibers in terms of the the Euler characteristics of the Hilbert scheme of points on the K3 surface and the NoetherLefschetz numbers of the fibration. Using this we prove the modularity of the DT invariants which was predicted in string theory. We develop a DTtheoretic conifold transition formula through which we compute the generating series for the invariants of Hilbert scheme of points for singular surfaces. We also use our geometric techniques to compute the generating series for DT invariants of threefolds given as complete intersections such as the quintic threefold. Finally if time permits I explain a connection between torsion DT invariants and higher dimensional Knot theory. 
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