Rational curves on wonderful compactifications of symmetric varieties
Arsen Shebzukhov
TL;DR
This paper investigates the structure of rational curves on wonderful compactifications of symmetric varieties, revealing irreducibility properties in specific cases and contributing to the understanding of their moduli spaces.
Contribution
It proves the non-irreducibility of the moduli space of rational curves on general wonderful compactifications and establishes irreducibility in the case of group compactifications.
Findings
Moduli space of rational curves is not irreducible in general.
In group compactifications, the set of rational curves with irreducible source is irreducible.
Provides new insights into the geometry of wonderful varieties and their rational curves.
Abstract
This work is a PhD thesis. First we provide some general context on wonderful varieties and moduli spaces of rational curves. Working over complex numbers we prove that the moduli space of rational curves with no marked points on the wonderful compactification of a symmetric space is not irreducible in general. Lastly we show that in the case of wonderful group compactifications the set of rational curves with no marked points and irreducible source is irreducible.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation