arXiv subjects

Jordi Hernández

Publications and source records attributed to Jordi Hernández.

2 recordsLinked to original sources

arXiv2024

The cubo-cubic transformation of the smooth quadric fourfold is very special

We classify special self-birational transformations of the smooth quadric threefold and fourfold, $Q^3$ and $Q^4$. It turns out that there is only one such example in each dimension. In the case of $Q^3$, it is given by the linear system of quadrics passing through a rational normal quartic curve. In the case of $Q^4$, it is given by the linear system of cubics passing through a non-minimal K3 surface of degree $10$ with two skew $(-1)$-lines.

math.AG↗

arXiv2024

A note on special cubic fourfolds of discriminant 14 and non-minimal K3 surfaces of degree 10

We prove that a general cubic in the Hassett divisor $\mathcal{C}_{14}$ of special cubic fourfolds of discriminant $14$ contains a non-minimal K3 surface of degree $10$ containing two skew $(-1)$-lines and contained in a smooth quadric hypersurface $Q^4\subseteq \mathbb{P}^5$, but not contained in any other (possibly of lower rank) quadric hypersurface.

math.AG↗