Marked Artin--Schelter surfaces of del Pezzo types

TL;DR

This paper introduces a new class of noncommutative surfaces called Artin--Schelter surfaces of del Pezzo types, generalizing classical del Pezzo surfaces, and explores their moduli spaces in relation to elliptic curves.

Contribution

It defines Artin--Schelter surfaces of del Pezzo types and establishes a birational equivalence between their moduli stacks and certain moduli of elliptic curves with line bundles.

Findings

Artin--Schelter surfaces of del Pezzo types include classical del Pezzo surfaces.

The moduli stacks of these surfaces are birational to moduli of elliptic curves with line bundles.

Provides a new perspective on noncommutative algebraic geometry related to del Pezzo surfaces.

Abstract

We introduce a class of noncommutative surfaces called Artin--Schelter surfaces of del Pezzo types, which contains del Pezzo surfaces as special cases. We show that the moduli stacks of marked Artin--Schelter surfaces of del Pezzo types are birational to the moduli stacks of tuples consisting of a smooth projective curve of genus 1, two line bundles of degree 3, and a collection of line bundles of degree 1 on the curve.