An explicit class of Lagrangian surfaces

TL;DR

This paper constructs a new family of algebraic surfaces with specific invariants, demonstrating they are Lagrangian in their Albanese variety and have a canonical map with particular properties.

Contribution

It introduces a novel family of general type surfaces with specified invariants that are Lagrangian in their Albanese variety and have a 2:1 canonical map onto a nodal surface.

Findings

Surfaces have invariants q=4, p_g=6, K^2=24.

Canonical map is 2:1 onto a degree 12 surface.

The surfaces are Lagrangian in their Albanese variety.

Abstract

We construct a family of general type surfaces with $q=4$, $p_g=6$ and $K^2=24$. These surfaces enjoy some interesting properties: they are Lagrangian in their Albanese variety and their canonical map is $2:1$ onto a degree $12$ surface in $\mathbb P^5$ with $44$ even nodes.