Algebraic surfaces with canonical map of degree 13 15 17 18 21 22

TL;DR

This paper constructs new minimal smooth algebraic surfaces of general type with specific canonical map degrees, using $bZ_3^2$-cover techniques over blow-ups of $bP^1 imes bP^1$, expanding the known examples in algebraic geometry.

Contribution

It introduces explicit constructions of algebraic surfaces with canonical map degrees 13, 15, 17, 18, 21, 22, which were previously unknown or unconstructed.

Findings

Constructed surfaces with canonical map degrees 13, 15, 17, 18, 21, 22

Used $bZ_3^2$-cover techniques over blow-ups of $bP^1 imes bP^1$

Provided explicit examples expanding the classification of algebraic surfaces

Abstract

In this note, we construct some minimal smooth surfaces of general type with canonical map of degree $ 13, 15, 17, 18, 21, 22 $. These surfaces are constructed as $ \mathbb{Z}_{3}^2$-covers of a blow-up of $ \mathbb{P}^1 \times \mathbb{P}^1 $.