# Equations and tropicalization of Enriques surfaces

## TL;DR

This paper explicitly computes equations for Enriques surfaces through involutions on K3 surfaces, explores their tropicalization, and links tropical homology to classical Hodge numbers, advancing understanding of their algebraic and tropical geometry.

## Contribution

It provides explicit equations for Enriques surfaces, analyzes their tropicalization, and connects tropical homology with Hodge theory, offering new insights into their geometric structure.

## Key findings

- Computed equations of Enriques surfaces via K3 involutions
- Analyzed tropicalization and computed tropical homology
- Linked tropical homology dimensions to Hodge numbers

## Abstract

In this article we explicitly compute equations of an Enriques surface via the involution on a K3 surface. We also discuss its tropicalization and compute the tropical homology, thus recovering a special case of the result of \cite{IKMZ}, and establish a connection between the dimension of the tropical homology groups and the Hodge numbers of the corresponding algebraic Enriques surface.