Algebraic Geometry Seminar
Valentino Tosatti
Northwestern
Nakamaye's theorem on complex manifolds
Abstract: A result of Nakamaye states that the augmented base locus of a
nef and big line bundle on a smooth projective variety over the complex
numbers equals its null locus, i.e. the union of all irreducible
subvarieties where the restriction of the bundle has volume zero. This was
later extended to R-divisors by Ein-Lazarsfeld-Mustata-Nakamaye-Popa, and
more recently there has been renewed interest in this theorem, especially
in positive characteristic.
I will discuss a different extension of this theorem, to all nef real
(1,1) classes on compact complex manifolds. The null locus of a (1,1)
class is defined in the same way as for a line bundle, but defining the
augmented base locus takes some work and was done by Boucksom (who called
it the non-Kahler locus). The main result I will discuss then says that on
any compact complex manifolds the null locus of any nef real (1,1) class
coincides with its non-Kahler locus. I will also mention some of the
consequences of this theorem. This is joint work with Tristan Collins.
Wednesday February 12, 2014 at 4:00 PM in SEO 427