BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rodrigo Salomão (UFF) DTSTART:20210915T183000Z DTEND:20210915T200000Z DTSTAMP:20260423T004758Z UID:BRAG/58 DESCRIPTION:Title: On the classification of fibrations by singular curves on unirational surfac es\nby Rodrigo Salomão (UFF) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nIn 1944 Zariski discovered that Bertini’s theorem on variable singular points is no longer true when we pass from a field o f characteristic zero to a field of positive characteristic. In other word s\, he found fibrations by singular curves\, which only exist in positive characteristic. Such fibrations are connected with many interesting phenom ena. For instance\, the extension of Enrique’s classification of surface s to positive characteristic (Bombieri and Mumford in 1976)\, the countere xamples of Kodaira vanishing theorem (Mukai in 2013 and Zheng in 2016) and the isolated singularities with infinity Milnor number (jointly work with Hefez and Rodrigues in 2019). In this talk we are going to show that the smoothing process introduced by Shimada in 1991 can be used to describe th e set of fibrations by genus two singular curves on unirational surfaces\, up to isomorphism among their generic fibers\, such that the smoothing ar e elliptic fibrations. Moreover we will also describe the vector fields wh ose tangencies with elliptic fibrations generate such fibrations by singul ar curves\, after the quotient of the rational elliptic surfaces. This is a work in progress with J. H. O. Rodrigues and R. O. C. Santos.\n LOCATION:https://researchseminars.org/talk/BRAG/58/ END:VEVENT END:VCALENDAR