O. Debarre
Gushel-Mukai varieties with many symmetries and an explicit
irrational Gushel-Mukai threefold
We construct an explicit complex smooth Fano threefold with Picard
number 1, index 1, and degree 10 (also known as a Gushel-Mukai
threefold) and prove that it is not rational by showing that its
intermediate Jacobian has a faithfull PSL(2,F11)
-action. Along the way, we construct Gushel-Mukai varieties of
various dimensions with rather large (finite) automorphism
groups. The starting point of all these constructions is an EPW
sextic with a faithful PSL(2,F11)
-action discovered by Giovanni Mongardi in his thesis in 2013 and
all this is joint work with him.
A. Pukhlikov
Rationally connected rational double covers of primitive Fano
varieties
We show that for a Zariski general hypersurface V of degree M+1 in
\mathbb PM+1 for M\geqslant 5 there are no Galois
rational covers X\dashrightarrow V with an abelian Galois group,
where X is a rationally connected variety. In particular, there are
no rational maps X\dashrightarrow V of degree 2 with X rationally
connected. This fact is true for many other families of primitive
Fano varieties as well and motivates a conjecture on absolute
rigidity of primitive Fano varieties.
A. Corti
Mori fibred Calabi-Yau pairs birational to (P3,
quartic surface)
We classify Mori fibred Calabi-Yau pairs in the title when the
surface has an A1 or A2 singularity.
I. Dolgachev
Automorphisms of Coble surfaces
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