CLASSIFICATION OF SMOOTH SCHUBERT VARIETIES IN THE SYMPLECTIC GRASSMANNIANS HONG, JAEHYUN;
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.
Schubert varieties;symplectic Grassmannians;
S. Billey and V. Lakshimibai, Singular loci of Schubert varieties, Progress in Mathematics 182, Birkhauser, 2000.
M. Brion and P. Polo, Generic singularities of certain Schubert varieties, Math. Z. 231 (1999), no. 2, 301-324.
J. Hong and N. Mok, Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds, J. Differential Geom. 86 (2010), no. 3, 539-567.
J. Hong and N. Mok, Characterization of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1, J. Algebraic Geom. 22 (2013), no. 2, 333-362.
J. Hong and K.-D. Park, Characterization of standard embeddings between rational homogeneous manifolds of Picard number 1, Int. Math. Res. Not. 2011 (2011), no. 10, 2351-2373.
J.-M. Hwang and N. Mok, Rigidity of irreducible Hermitian symmetric spaces of the compact type under Kahler deformation, Invent. Math. 131 (1998), no. 2, 393-418.
J.-M. Hwang and N. Mok, Deformation rigidity of the 20-dimensional $F_4$-homogeneous space associated to a short root, In: Algebraic transformation groups and algebraic varieties, pp. 37-58, Encyclopedia Math. Sci., 132, Springer-Verlag, Berlin, 2004.
J.-M. Hwang and N. Mok, Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kahler deformation, Invent. Math. 160 (2005), no. 3, 591-645.
V. Lakshmibai and J. Weyman, Multiplicities of points on a Schubert variety in a minuscule G/P, Adv. Math. 84 (1990), no. 2, 179-208.
I. A. Mihai, Odd symplectic manifolds, Transformation Groups 12 (2007), no. 3, 573-599.