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Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
The Sarkisov program
James McKernan
UCSB
Friday, June 1, 2007, 4:00 p.m.
Room 6635 South Hall
Note Unusual Time
Abstract: The conjectural output of the minimal model program is either a minimal
model or a Mori fibre space. Unfortunately the output in neither case is unique.
Kawamata has recently shown that any two minimal models are connected by
a sequence of flops. The Sarkisov program aims to factorise any birational map
between two Mori fibre spaces into a sequence of elementary links. In the case of
surfaces, an elementary transformation of P1
-bundles is an example of such a link,
and the Sarkisov program provides a natural framework to prove that the birational
automorphism group of P2
is generated by a Cremona transformation and PGL(3).
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