Picard 秩十六的广义 Inose 四次曲面上 Jacobian 椭圆纤维化

Generalized Shioda-Inose Structures on K3 Surfaces

We examine the finite group actions on K3 and Abelian surfaces giving the same orbit space after desingularization. We show that when the group is not Z_2, then the Picard number of the K3 surface must be 19 or 20, and that in the latter case the Abelian surface is uniquely determined by the K3 surface.

关于自同构群为$\u200b\mathrm{Aut}(\mathcal{X})=(\mathbb{Z}/2\mathbb{Z})^2$的射影K3曲面$\mathcal{X}$

On projective K3 surfaces $\mathcal{X}$ with $\mathrm{Aut}(\mathcal{X})=(\mathbb{Z}/2\mathbb{Z})^2$

该数学代数几何领域的研究证明了自同构群为$(\mathbb{Z}/2\mathbb{Z})^2$的K3曲面存在双六次曲面形式的显式双有理模型，还在皮卡数大于9时得到推广Inose四次曲面的射影四次超曲面第二模型。

On some K3 surfaces with order sixteen automorphism

We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We show that all of these K3 surfaces admit an elliptic fibration and we compute the invariant lattices in a geometric way by using special curves of the elliptic fibration. The computation of these lattices plays an important role when one wants to study moduli spaces and mirror symmetry for lattice polarized K3 surfaces.

Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell--Yan scattering

We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda--Inose structure. Moreover, we point out the physical relevance of our results.

整数系数下不变循环定理的失效

Failure of the invariant cycle theorem over $\mathbb Z$

研究1参数半稳定变种族的局部不变循环定理，证明H¹总成立，H²在一般纤维Albanese变种 trivial 时成立，构造首个整数系数下失效的半稳定族，涉及非平凡Albanese变种和最大Picard秩。

Six line configurations and string dualities

We study the family of K3 surfaces of Picard rank sixteen associated with the double cover of the projective plane branched along the union of six lines, and the family of its Van Geemen-Sarti partners, i.e., K3 surfaces with special Nikulin involutions, such that quotienting by the involution and blowing up recovers the former. We prove that the family of Van Geemen-Sarti partners is a four-parameter family of K3 surfaces with $H \oplus E_7(-1) \oplus E_7(-1)$ lattice polarization. We describe explicit Weierstrass models on both families using even modular forms on the bounded symmetric domai…