Exceptional hereditary curves and real curve orbifolds

TL;DR

This paper develops the theory of exceptional hereditary curves over arbitrary fields, linking them to wallpaper groups and real curve orbifolds, and proves the existence of tilting objects in specific cases.

Contribution

It introduces a comprehensive framework for exceptional hereditary curves over arbitrary fields and connects them to wallpaper groups and real orbifolds, expanding existing mathematical theories.

Findings

Existence of tilting objects on certain hereditary curves

Connection established between wallpaper groups and real hereditary curves

Enhanced understanding of equivariant sheaves on genus zero quotient curves

Abstract

In this paper, we elaborate the theory of exceptional hereditary curves over arbitrary fields. In particular, we study the category of equivariant coherent sheaves on a regular projective curve whose quotient curve has genus zero and prove existence of a tilting object in this case. We also give a link between wallpaper groups and real hereditary curves, providing details to an old observation made by Helmut Lenzing.