Exceptional collections on Dolgachev surfaces associated with degenerations
Yongnam Lee (Kaist)
Aula Beltrami - Tuesday, February 23, 2016 h.14:30
Abstract. Abstract:
Dolgachev surfaces are simply connected minimal elliptic surfaces with $p_g=q=0$ and of Kodaira dimension 1. These surfaces were constructed by logarithmic transformations of rational elliptic surfaces. Dolgachev surfaces can be also constructed via Q-Gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities based on the construction by Lee-Park. In this talk, some exceptional bundles and collections on Dolgachev surfaces associated with Q-Gorenstein smoothing will be constructed based on the idea of Hacking. Furthermore, in the case if Dolgachev surfaces were of type (2, 3), we describe the Picard group and present an exceptional collection of maxiaml length. Finally, we prove that the presented exceptional collection gives a nontrivial phantom category. This is a joint work with Yonghwa Cho.
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602