A surface with canonical map of degree $24$

TL;DR

This paper constructs a complex algebraic surface with specific invariants, notably a canonical map of degree 24 onto the projective plane, expanding understanding of surfaces with high-degree canonical maps.

Contribution

It presents the first known example of a surface with a canonical map of degree 24 onto ^2, with particular invariants, demonstrating new possibilities in surface classification.

Findings

Constructed a surface with p_g=3, q=0, K^2=24

Achieved a canonical map of degree 24 onto ^2

Provides a new example in the classification of algebraic surfaces

Abstract

We construct a complex algebraic surface with geometric genus $p_g=3$, irregularity $q=0$, self-intersection of the canonical divisor $K^2=24$ and canonical map of degree $24$ onto $\mathbb P^2$.