Fano-Mukai fourfolds of genus $10$ as compactifications of ${\mathbb{C}}^4$

Yuri Prokhorov, Mikhail Zaidenberg

It is known that the moduli space of smooth Fano-Mukai fourfolds $V_{18}$ of genus $10$ has dimension one. We show that any such fourfold is a completion of ${\mathbb{C}}^4$ in two d…