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BEGIN:VEVENT
SUMMARY:On the unirationality of del Pezzo surfaces of degree 2
DTSTART:20121025T111500
DTEND:20121025T123000
DTSTAMP:20260916T014035Z
UID:b9874cb61b1bc5e09e2103cb03eac64518aae14cad4904c79a1601d8
CATEGORIES:Conferences - Seminars
DESCRIPTION:Anthony Varilly-Alvarado\nLet k be a field and let X be a del 
 Pezzo surface of degree at least 3 over k. By work of Segre\, Manin and Ko
 ll'ar\, it is known that X is k-unirational as soon as X(k) is not empty. 
 When X is a surface of degree 2\, Manin showed that if X has a k-point lyi
 ng outside an explicit closed subset of X\, then X is k-unirational. A clo
 se inspection of Manin's proof reveals that the explicit closed subset to 
 be ignored is larger than originally thought. We will discuss some improve
 ments on this closed subset and use it to show that when k is finite\, all
  but four surfaces in characteristic 3 are provably k-unirational. One of 
 the surfaces that eludes analysis is a nontrivial quadratic twist of the d
 ouble cover of the plane ramified along the Fermat curve x4 + y4 + z4 = 0\
 , over F_9. I will explain why the beautiful and pathological geometry of 
 this surface make it a suitable departure point for further study on k-uni
 rationality of del Pezzo surfaces of degree 2. This is joint work with Cec
 ilia Salgado and Damiano Testa.
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 nem
STATUS:CONFIRMED
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