# Project Tropical Singularities

## Basic data

Title:

Tropical Singularities

Duration:

01/03/2016 to 01/12/2017

Abstract / short description:

In tropical geometry, algebraic varieties are degenerated to polyhedral complexes called tropical varieties. In spite of the degeneration, many properties of an algebraic variety can be read off its tropical counterpart, and many theorems continue to hold on the tropical side. Tropical geometry thus provides an approach to study questions in algebraic geometry by means of discrete mathematics and combinatorics. Tropical geometry has been succesfully applied to computational problems and problems in enumerative geometry, in particular real enumerative questions.

To really make good use of the new tool, many questions of translating nature have to be answered. The central question for this project is: what is the correct translation of the concept of a singularity to the tropical world?

This question is quite natural to ask and has consequently interested several authors recently. The fact that it is hard to answer in general makes it even more intriguing. The aim of this project is to considerably improve the understanding of tropical singularities, to apply the results to questions in enumerative geometry, and to investigate the connections of this subject to questions in combinatorics.

To really make good use of the new tool, many questions of translating nature have to be answered. The central question for this project is: what is the correct translation of the concept of a singularity to the tropical world?

This question is quite natural to ask and has consequently interested several authors recently. The fact that it is hard to answer in general makes it even more intriguing. The aim of this project is to considerably improve the understanding of tropical singularities, to apply the results to questions in enumerative geometry, and to investigate the connections of this subject to questions in combinatorics.

Keywords:

geometry

Geometrie

algebraic geometry

Algebraische Geometrie

## Involved staff

### Managers

Department of Mathematics

Faculty of Science

Faculty of Science

## Local organizational units

Department of Mathematics

Faculty of Science

University of Tübingen

University of Tübingen

## Funders

Bonn, Nordrhein-Westfalen, Germany