arXiv subjects

Frédéric Han

Publications and source records attributed to Frédéric Han.

3 recordsLinked to original sources

arXiv2020

Hilbert squares of K3 surfaces and Debarre-Voisin varieties

The Debarre-Voisin hyperkähler fourfolds are built from alternating $3$-forms on a $10$-dimensional complex vector space, which we call trivectors. They are analogous to the Beauville-Donagi fourfolds associated with cubic fourfolds. In this article, we study several trivectors whose associated Debarre-Voisin variety is degenerate, in the sense that it is either reducible or has excessive dimension. We show that the Debarre-Voisin varieties specialize, along general $1$-parameter degenerations to these trivectors, to varieties isomorphic or birationally isomorphic to the Hilbert square of a K3 surface.

math.AG↗

arXiv2017

Quarto-quartic birational maps of $\mathbb{P}_3(\mathbb{C})$

We construct a determinantal family of quarto-quartic transformations of a complex projective space of dimension $3$ from trigonal curves of degree $8$ and genus $5$. Moreover we show that the variety of $(4,4)$-birational maps of $\mathbb{P}_3(\mathbb{C})$ has at least four irreducible components and describe three of them.

math.AG↗

arXiv2015

On cubic birational maps of $\mathbb{P}^3_\mathbb{C}$

We study the birational maps of $\mathbb{P}^3_\mathbb{C}$. More precisely we describe the irreducible components of the set of birational maps of bidegree $(3,3)$ (resp. $(3,4)$, resp. $(3,5)$).

math.AG↗