The Chow Rings of Generalized Grassmannians
نویسندگان
چکیده
Based on the Basis theorem of Bruhat–Chevalley [C] and the formula for multiplying Schubert classes obtained in [Du] and programed in [DZ1], we introduce a new method computing the Chow rings of flag varieties (resp. the integral cohomology of homogeneous spaces). The method and results of this paper have been extended in [DZ3, DZ4] to obtain the integral cohomology rings of all complete flag manifolds, and to construct the integral cohomologies of Lie groups in terms of Schubert classes. 2000 Mathematical Subject Classification: 14M15; 57T15.
منابع مشابه
The Chow rings of generalized Grassmanianns
Based on the formula for multiplying Schubert classes obtained in [D2] and programed in [DZ1], we introduce a new method to compute the Chow ring of a flag variety G/H . As applications the Chow rings of some generalized Grassmannians G/H are presented as the quotients of polynomial rings in the special Schubert classes on G/H .
متن کاملAn Additive Basis for the Chow Ring of M 0 , 2 ( P r , 2 )
We begin a study of the intersection theory of the moduli spaces of degree two stable maps from two-pointed rational curves to arbitrary-dimensional projective space. First we compute the Betti numbers of these spaces using Serre polynomial and equivariant Serre polynomial methods developed by E. Getzler and R. Pandharipande. Then, via the excision sequence, we compute an additive basis for the...
متن کاملOn Generic Quadratic Forms
Based on Totaro’s computation of the Chow ring of classifying spaces for orthogonal groups, we compute the Chow rings of all orthogonal Grassmannians associated with a generic quadratic form of any dimension. This closes the gap between the known particular cases of the quadric and the highest orthogonal Grassmannian. We also relate two different notions of generic quadratic forms.
متن کاملTransformations of Grassmannians and automorphisms of classical groups
We consider transformations preserving certain linear structure in Grassmannians and give some generalization of the Fundamental Theorem of Projective Geometry and the Chow Theorem [Ch]. It will be exploited to study linear (k, n − k)-involutions, 1 < k < n − 1. The analogy of the J. Dieudonné and C. E. Rickart result will be obtained.
متن کاملThe Minimal Degeneration Singularities in the Affine Grassmannians
The minimal degeneration singularities in the affine Grassmannians of simple simply-laced algebraic groups are determined to be either Kleinian singularities of type A, or closures of minimal orbits in nilpotent cones. The singularities for non-simply-laced types are studied by intersection cohomology and equivariant Chow group methods.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Foundations of Computational Mathematics
دوره 10 شماره
صفحات -
تاریخ انتشار 2010