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SUMMARY:Cesar Hilario (IMPA)
DTSTART:20210426T200000Z
DTEND:20210426T210000Z
DTSTAMP:20260423T035918Z
UID:AGSAGS/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGSAGS/28/">
 Bertini's theorem in positive characteristic</a>\nby Cesar Hilario (IMPA) 
 as part of American Graduate Student Algebraic Geometry Seminar\n\n\nAbstr
 act\nThe Bertini-Sard theorem is a classical result in algebraic geometry.
  It states that in characteristic zero almost all the fibers of a dominant
  morphism between two smooth algebraic varieties are smooth\; in other wor
 ds\, there do not exist fibrations by singular varieties with smooth total
  space. Unfortunately\, the Bertini-Sard theorem fails in positive charact
 eristic\, as was first observed by Zariski in the 1940s. Investigating thi
 s failure naturally leads to the classification of its exceptions. By a th
 eorem of Tate\, a fibration by singular curves of arithmetic genus g in ch
 aracteristic p > 0 may exist only if p <= 2g + 1. When g = 1 and g = 2\, t
 hese fibrations have been studied by Queen\, Borges Neto\, Stohr and Simar
 ra Canate. A birational classification of the case g = 3 was started by St
 ohr (p = 7\, 5)\, and then continued by Salomao (p = 3). In this talk I wi
 ll report on some progress in the case g = 3\, p = 2. In fact\, a great va
 riety of examples exist and very interesting geometric phenomena arise fro
 m them.\n
LOCATION:https://researchseminars.org/talk/AGSAGS/28/
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