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CLASSIFICATION OF SMOOTH SCHUBERT VARIETIES IN THE SYMPLECTIC GRASSMANNIANS

홍재현
대한수학회 (The Korean Mathematical Society)|2015.09|대한수학회지 (Journal of the KMS)|제52권 제5호|pp. 1109-1122

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참고문헌

키워드

Schubert varietiessymplectic Grassmannians
주제분류수학

초록

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.

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.

참고문헌 (10)

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  3. J. Hong, "Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds", J. Differential Geom, 86(3), pp.539~567 (2010)
  4. J. Hong, "Characterization of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1", J. Algebraic Geom, 22(2), pp.333~362 (2013)
  5. J. Hong, "Characterization of standard embeddings between rational homogeneous manifolds of Picard number 1", Int. Math. Res. Not, 2011(10), pp.2351~2373 (2011)
  6. J.-M. Hwang, "Rigidity of irreducible Hermitian symmetric spaces of the compact type under K¨ahler deformation", Invent. Math, 131(2), pp.393~418 (1998)
  7. J.-M. Hwang, "Deformation rigidity of the 20-dimensional F4-homogeneous space associated to a short root, In: Algebraic transformation groups and algebraic varieties", Encyclopedia Math. Sci., 132, pp.37~58 (2004), Springer-Verlag
  8. J.-M. Hwang, "Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under K¨ahler deformation", Invent. Math, 160(3), pp.591~645 (2005)
  9. V. Lakshmibai, "Multiplicities of points on a Schubert variety in a minuscule G", P, 1990, pp.84(2), 179~208
  10. I. A. Mihai, "Odd symplectic manifolds", Transformation Groups, 12(3), pp.573~599 (2007)

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