Semistable K3-surfaces with icosahedral symmetry

Quartic double solids with icosahedral symmetry

We study quartic double solids admitting icosahedral symmetry.

Quartic surfaces with icosahedral symmetry

We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.

关于具有半稳定退化的紧复流形的Hodge结构

On Hodge structures of compact complex manifolds with semistable degenerations

研究半稳定退化紧复流形上Hodge理论性质的保持条件，证明在特定单值性条件下，Hodge对称性和Hodge-Riemann关系成立。

The icosahedral line configuration and Waldschmidt constants

There is a highly special point configuration in $\mathbb{P}^2$ of 31 points, naturally arising from the geometry of the icosahedron. The 15 planes of symmetry of the icosahedron projectivize to 15 lines in $\mathbb{P}^2$, whose points of intersections yield the 31 points. Each point corresponds to an opposite pair of vertices, faces or edges of the icosahedron. The symmetry group of the icosahedron is $G=A_5\times \mathbb{Z}_2$, one of finitely many exceptional complex reflection groups. The action of $G$ on the icosahedron descends onto an action on the line configuration. We blow up $\mathb…

On K3 fibrations: towards mirror symmetry

Given X a K3 surface, a mirror dual to X can be identified with a component of the moduli space of semistable sheaves on X. We consider fibrations by K3 surfaces over a one dimensional base that are Calabi-Yau and we charaterize the dual fibration that turns to be derived equivalent to the original one relating the problem to mirror symmetry.

On K3 fibered Calabi-Yau 3-folds

Given X a K3 surface, a mirror dual to X can be identified with a component of the moduli space of semistable sheaves on X. We consider fibrations by K3 surfaces over a one dimensional base that are Calabi-Yau and we obtain a dual fibration that turns to be derived equivalent to the original one and we relate the problem to mirror symmetry.