Intersection numbers on Grassmannians, and on the space of holomorphic maps from CP1 into Gr(Cn)
✍ Scribed by Noureddine Chair
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 104 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0393-0440
No coin nor oath required. For personal study only.
✦ Synopsis
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 Grassmannian 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.