A Note of Hodge's Postulation Formula for Schubert Varieties
A Note of Hodge's Postulation Formula for Schubert
Varieties1
Sudhir R. Ghorpade
2
Department of Mathematics
Indian Institute of Technology, Bombay
Powai, Mumbai 400076 India
E-mail: srg@math.iitb.ernet.in
May 25, 2000
Abstract
In this note we give a somewhat simpler description and an alternative proof
of the so called postulation formula , due to Hodge, which explicitly
gives the Hilbert function as well as the Hilbert polynomial of Schubert
varieties in Grassmannians. Our proof uses the combinatorics of
nonintersecting lattice paths and a mild generalization of a result of
Gessel and Viennot. The necessary background concerning such lattice paths
is also presented in a self-contained manner.
Contents
| 1 | Introduction | 1 |
| 2 | Schubert Varieties in Grassmannians | 2 |
| 3 | Nonintersecting Lattice Paths | 3 |
| 4 | Hodge's Postulation Formula | 5 |
| | References | 8 |
1
2000 Mathematics Subject Classification. Primary 14M15,
13D40, 05A15; Secondary 13P10, 14M12.
2
Partially
supported by a `Career Award' grant from AICTE,
New Delhi and an IRCC grant from IIT Bombay.
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