Wednesday December 2nd, 2020 | |
| Time: | 3:00 PM - 4:15 PM |
| Title: | Holomorphic 1-forms on the moduli space of curves |
| Speaker: | Gian Pietro Pirola , $\text{Università}$ degli studi di Pavia |
| Abstract: | |
| It is well known that there are no nontrivial closed 1-forms on the moduli space of curves of genus g>2. We show that if g>4 there are no nontrivial holomorphic one forms. We use both Satake and Deligne-Mumford compactifications of the moduli space and an extension result for the sections of a vector bundle F. More precisely we give a characterization for the surjectivety of the restriction map H^0(F)->H^0(F_D), here D is a divisor in a linear system |nH|, where n>>0 and H is a big and semiample line bundle. These results were obtained in collaboration with Filippo Favale and Sara Torelli. | |