

Iskovskikh Seminar
February 18, 2016 18:00, Moscow, Steklov Mathematical Institute, room 540






Unirationality of Uenotype manifold $X_{4,6}$ (following F. Catanese, K.
Oguiso, A. Verra)
A. S. Trepalin^{} ^{} Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow

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Abstract:
An Uenotype manifold is a minimal resolution of singularities of the
quotient of the manifold $E(6)^n$ by cyclic group of order $6$, where $E(6)$
is the elliptic curve given by the equation $y^2z = x^3  z^3$ in $P^2$ and
the group acts on each factor as $(x : y : z) \mapsto (\omega x : y : z)$
($\omega = e^{\frac{2\pi}{3}}$). We prove that Uenotype manifold $X_{4,6}$
is unirational if the ground field $k$ is not of characteristic $3$ and
contains $\omega$. By some technical computation we show that
unirationality of $X_{4,6}$ follows from unirationality of certain cubic
surface over the functional field $k(s_3, s_4)$. Then we prove
unirationality of this cubic surface.

