On K3 surfaces of Picard rank 14
نویسندگان
چکیده
We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist, namely $H \oplus E_8(-1) A_1(-1)^{\oplus 4}$, D_4(-1)$, D_8(-1) D_4(-1)$. As part of our study, we provide birational models for these as quartic projective hypersurfaces describe the associated coarse moduli spaces in terms suitable modular invariants. Additionally, explore connection between families dual related via Nikulin construction.
منابع مشابه
K3 Surfaces of Picard Rank One and Degree Two
Examples 1. A K3 surface of degree two is a double cover of P, ramified in a smooth sextic. K3 surfaces of degree four are smooth quartics in P. A K3 surface of degree six is a smooth complete intersection of a quadric and a cubic in P. And, finally, K3 surfaces of degree eight are smooth complete intersections of three quadrics in P. The Picard group of a K3 surface is isomorphic to Zn where n...
متن کاملPicard Lattices of Families of K3 Surfaces
Picard Lattices of Families of K3 Surfaces bysarah-marie belcastro Chair: Igor Dolgachev It is a nontrivial problem to determine the Picard Lattice of a given surface; theobject of this thesis is to compute the Picard Lattices of M. Reid’s list of 95 fami-lies of Gorenstein K3 surfaces which occur as hypersurfaces in weighted projectivespace. Reid’s list arises in many problems;...
متن کاملPicard Groups on Moduli of K3 Surfaces with Mukai Models
We discuss the Picard group of the moduli space Kg of quasi-polarized K3 surfaces of genus g ≤ 12 and g 6= 11. In this range, Kg is unirational, and a general element in Kg is a complete intersection with respect to a vector bundle on a homogenous space, by the work of Mukai. In this paper, we find generators for the Picard group PicQ(Kg) using Noether-Lefschetz theory. This verifies the Noethe...
متن کاملOn the computation of the Picard group for K3 surfaces
We construct examples of K3 surfaces of geometric Picard rank 1. Our method is a refinement of that of R. van Luijk [vL]. It is based on an analysis of the Galois module structure on étale cohomology. This allows to abandon the original limitation to cases of Picard rank 2 after reduction modulo p. Furthermore, the use of Galois data enables us to construct examples which require significantly ...
متن کاملHigher Rank Stable Pairs on K3 Surfaces
We define and compute higher rank analogs of PandharipandeThomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi-Yau threefolds have been defined by Sheshmani [She11b, She11a] using moduli of pairs of the form On → F for F purely one-dimensional and computed via wall-crossing techniques. These invariants may be thought of as virtually c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2023
ISSN: ['1522-2616', '0025-584X']
DOI: https://doi.org/10.1002/mana.202200197