Flexibility of Schubert classes
نویسندگان
چکیده
منابع مشابه
Flexibility of Schubert Classes
In this note, we discuss the flexibility of Schubert classes in homogeneous varieties. We give several constructions for representing multiples of a Schubert class by irreducible subvarieties. We sharpen [R, Theorem 3.1] by proving that every positive multiple of an obstructed class in a cominuscule homogeneous variety can be represented by an irreducible subvariety.
متن کاملMultiplicative rule of Schubert classes
Let G be a compact connected Lie group and H, the centralizer of a one-parameter subgroup in G. Combining the ideas of Bott-Samelson resolutions of Schubert varieties and the enumerative formula on a twisted product of 2 spheres obtained in [Du2], we obtain a closed formula for multiplying Schubert classes in the flag manifold G/H. 2000 Mathematical Subject Classification: 14N15 (14M10).
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Let G be a compact connected Lie group andH the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan
متن کاملAlgorithm for Multiplying Schubert Classes
Based on the multiplicative rule of Schubert classes obtained in [Du3], we present an algorithm computing the product of two arbitrary Schubert classes in a flag variety G/H, where G is a compact connected Lie group and H ⊂ G is the centralizer of a one-parameter subgroup in G. Since all Schubert classes on G/H constitute an basis for the integral cohomology H∗(G/H), the algorithm gives a metho...
متن کاملRigidity of Schubert Classes in Orthogonal Grassmannians
A Schubert class σ in the cohomology of a homogeneous variety X is called rigid if the only projective subvarieties of X representing σ are Schubert varieties. A Schubert class σ is called multi rigid if the only projective subvarieties representing positive integral multiples of σ are unions of Schubert varieties. In this paper, we discuss the rigidity and multi rigidity of Schubert classes in...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2013
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2013.09.003