Explicit Computations for the Intersection Numbers on Grassmannians, and on the Space of Holomorphic Maps from CP^1 into G_r(C^n)

Noureddine Chair

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Explicit Computations for the Intersection Numbers on Grassmannians, and on the Space of Holomorphic Maps from CP^1 into G_r(C^n)

Noureddine Chair

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Abstract

We derive some explicit expressions for correlators on Grassmannian G_r(C^n) as well as on the moduli space of holomorphic maps, of a fixed degree d, from sphere into the Grassmannian. Correlators obtained on the Grassmannain are a first step generalization of the Schubert formula for the self-intersection. The intersection numbers on the moduli space for r=2,3 are given explicitly by two closed formulas, when r=2 the intersection numbers, are found to generate the alternate Fibonacci numbers, the Pell numbers and in general a random walk of a particle on a line with absorbing barriers. For r=3 the intersection numbers form a well organized pattern.

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Noureddine Chair. 1998-08-27. Explicit Computations for the Intersection Numbers on Grassmannians, and on the Space of Holomorphic Maps from CP^1 into G_r(C^n). https://arxiv.org/abs/hep-th/9808170

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