an afternoon of algebraic geometry

[Barbara Fantechi]

Next Wednesday, July 10, in room 136 at Sissa:
15:30 Cristina Manolache, Mirror Symmetry without localization
17:00 Alex Massarenti, Mori Dream Spaces obtained by blowing-up
points in projective spaces.

Abstract of Massarenti's talk: The goal of the minimal model program
is to construct a
birational model of any complex projective variety which is as simple
as possible in a suitable sense. This subject has its origins in the
classical birational geometry of surfaces studied by the Italian
school. In 1988 S. Mori extended the concept of minimal model to
3-folds by allowing suitable singularities on them. In 2010 there was
a great breakthrough in the minimal model theory when C. Birkar, P.
Cascini, C. Hacon and J. McKernan proved the existence of minimal
models for varieties of log general type.
Mori Dream Spaces, introduced by Y. Hu and S. Keel in 2002, form a
class of algebraic varieties that behave very well from the point of
view of Mori's minimal model program. They can be algebraically
characterized as varieties whose total coordinate ring, called the Cox
ring, is finitely generated.
In addition to this algebraic characterization there are several
algebraic varieties characterized by some positivity property of the
anti-canonical divisor, such as weak Fano and log Fano varieties, that
turn out to be Mori Dream Spaces. In this talk, I will show how to
obtain log Fano varieties and Mori Dream Spaces by blowing-up
projective spaces in a certain number of general points.

-- 
Mathematical Physics Sector
Sissa
Via Bonomea 265
34136 Trieste
tel +390403787325 fax +390403787528
public calendar: http://people.sissa.it/fantechi/cal