Fwd: Seminar by Fedor Bogomolov - Thur 13 June 2019, 2:00 pm

[Jacopo Stoppa]

Dear all,

on Thursday 13 June at 2:00 pm in room 005 of SISSA, Prof. Fedor Bogomolov
(Courant and HSE) will give the seminar:

"On the base of a lagrangian fibration for a compact hyperkahler manifold"

Abstract: In my talk I will discuss our proof with N. Kurnosov that the
base of such fibration for complex projective hyperkahler manifold of
complax  dimension $4$ is always a projective plane $P^2$. In fact we show
that the base of such fibration can not have a singular point of type
$E_8$. It was by the theorem of Matsushita and others that only quotient
singularities can occur and if the base is smooth then the it is isomorphic
to $P^2$. The absence of other singualrities apart from $E_8$ has been
already known and we show that $E-8$ can not occur either. Our method can
be applied to other types of singularities
for the study of  lagrangian fibrations in higher dimensions. More recently
similar result was obtained by Huybrechts and Xu.

All best,
Jacopo