Wonderful Varieties: A geometrical realization
S. Cupit-Foutou
TL;DR
This paper provides a geometric realization of wonderful varieties using invariant Hilbert schemes and proves Luna's conjecture that classifies these varieties via spherical systems.
Contribution
It introduces a geometric construction of wonderful varieties and confirms Luna's conjecture linking them to spherical systems.
Findings
Wonderful varieties are realized through invariant Hilbert schemes.
Luna's conjecture on classification by spherical systems is proven.
The work bridges geometric and combinatorial approaches to these varieties.
Abstract
A geometrical realization of wonderful varieties by means of a suitable class of invariant Hilbert schemes is given. As a consequence, Luna's conjecture asserting that wonderful varieties are classified by spherical systems, triples of combinatorial invariants, is proved.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory