September 18, 2025Open Access

Embedding of lattices and K3-covers of an enriques surface

Key Points

Necessary conditions for the embedding of lattices are established, leading to insights into K3 and Enriques surfaces.
The approach refines existing criteria and introduces a more elementary perspective on surface structures.
Results extend to any lattices, providing a comprehensive framework for embedding conditions.
Understanding these embeddings may improve our theoretical grasp of the algebraic characteristics of K3 surfaces.

Abstract

Abstract In this study, we establish necessary conditions for the embeddings of lattices and apply these conditions to the problem of characterizing algebraic K 3 K3 surfaces that cover an Enriques surface. By refining existing criteria and providing a more elementary approach, we offer a new perspective on the structure of such surfaces. Our results apply to any lattices, extending beyond specific cases and offering a comprehensive framework for understanding the embedding conditions in terms of Gram matrices.

Embedding of lattices and K3-covers of an enriques surface

Key Points

Abstract

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