Recent developments and open problems in linear series

TL;DR

This paper compiles recent developments, open problems, and discussions from a workshop on linear series in algebraic varieties, aiming to serve as an accessible resource for researchers in the field.

Contribution

It provides a collection of problems, examples, and results related to linear series, consolidating scattered literature and folklore into an organized, accessible format.

Findings

Compilation of open problems and results in linear series

Examples and discussions from the 2010 Oberwolfach workshop

Identification of gaps and future directions in the field

Abstract

In the week 3--9, October 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted a mini workshop Linear Series on Algebraic Varieties. These notes contain a variety of interesting problems which motivated the participants prior to the event, and examples, results and further problems which grew out of discussions during and shortly after the workshop. A lot of arguments presented here are scattered in the literature or constitute folklore. It was one of our aims to have a usable and easily accessible collection of examples and results.