On geometric properties of orbital varieties in type A

Lucas Fresse, Anna Melnikov

Research output: Contribution to journalArticlepeer-review


The intersection between a nilpotent orbit O∪gln(C) and the Lie algebra Lie(B)∪gln(C) of a Borel subgroup B∪GLn(C) is an equidimensional, quasi-affine algebraic variety. Its irreducible components are called orbital varieties. In this Note, we provide criteria to guarantee that an orbital variety is smooth or has a dense orbit for the adjoint action of B. In addition, we point out a possible relation between these two properties.

Original languageEnglish
Pages (from-to)735-739
Number of pages5
JournalComptes Rendus Mathematique
Issue number13-14
StatePublished - Jul 2011

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (L. Fresse), [email protected] (A. Melnikov). 1 Supported by the European project GLC, ERC grant No. 247049.

ASJC Scopus subject areas

  • General Mathematics


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