Classification of smooth Schubert varieties in the symplectic Grassmannians

Jaehyun Hong

doi:10.4134/JKMS.2015.52.5.1109

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2015; 52(5): 1109-1122

Printed September 1, 2015

https://doi.org/10.4134/JKMS.2015.52.5.1109

Classification of smooth Schubert varieties in the symplectic Grassmannians

Jaehyun Hong

Seoul National University

Abstract

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Abstract

A Schubert variety in a rational homogeneous variety $G/P$ is defined by the closure of an orbit of a Borel subgroup $B$ of $G$. In general, Schubert varieties are singular, and it is an old problem to determine which Schubert varieties are smooth. In this paper, we classify all smooth Schubert varieties in the symplectic Grassmannians.

Keywords: Schubert varieties, symplectic Grassmannians

MSC numbers: Primary 14Mxx, 53Cxx