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CHERN CLASS FORMULAS FOR G2 SCHUBERT LOCI DAVE ANDERSON
 

Summary: CHERN CLASS FORMULAS FOR G2 SCHUBERT LOCI
DAVE ANDERSON
Abstract. We define degeneracy loci for vector bundles with structure
group G2, and give formulas for their cohomology (or Chow) classes in terms
of the Chern classes of the bundles involved. When the base is a point,
such formulas are part of the theory for rational homogeneous spaces devel-
oped by Bernstein­Gelfand­Gelfand and Demazure. This has been extended
to the setting of general algebraic geometry by Giambelli­Thom­Porteous,
Kempf­Laksov, and Fulton in classical types; the present work carries out
the analogous program in type G2. We include explicit descriptions of the G2
flag variety and its Schubert varieties, and several computations, including
one that answers a question of W. Graham.
In appendices, we collect some facts from representation theory and com-
pute the Chow rings of quadric bundles, correcting an error in [Ed-Gr].
Contents
1. Introduction 1
2. Overview 4
3. Octonions and compatible forms 9
4. Topology of G2 flags 15
5. Cohomology of flag bundles 18

  

Source: Anderson, Dave - Department of Mathematics, University of Washington at Seattle

 

Collections: Mathematics