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


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.


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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