Back to Algebraic Geometry Seminar: Spring 2025
Algebraic Geometry Seminar
Date: Tuesday, Apr 1, 2025
Time: 3:30PM - 4:30PM
Location: LCB 225
Ben Church
Stanford
Title |
Nowhere vanishing 1-forms on varieties admitting a good minimal model |
Abstract |
A theorem of Popa and Schnell shows that if a smooth projective variety X admits a 1-form with no zeros it cannot be of general type. However, one expects far more stringent constraints on the geometry of those X actually admitting nonvanishing 1-forms. If X is not uniruled and assuming the conjectures of MMP, we show that X is birational to an isotrivial fibration over an abelian variety. This partially answers conjectures of Hao–Schreieder, Meng–Popa, and Chen–Church–Hao. The proof involves a decomposition result for families of Calabi-Yau varieties surjecting onto a fixed abelian variety. If X is uniruled, we also give a weak structure theorem that relies on using higher direct image Hodge modules in the method of Popa–Schnell. |
Algebraic Geometry