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Multiplicity-Free Schubert Calculus |
Canad. Math. Bull. 53(2010), 171-186
Published:2009-12-04
Printed: Mar 2010
Printed: Mar 2010
- Hugh Thomas
- Alexander Yong
Abstract
Multiplicity-free algebraic geometry is the study of subvarieties
$Y\subseteq X$ with the ``smallest invariants'' as witnessed by a
multiplicity-free Chow ring decomposition of
$[Y]\in A^{\star}(X)$ into a predetermined
linear basis.
This paper concerns the case of Richardson subvarieties of the Grassmannian
in terms of the Schubert basis. We give a nonrecursive combinatorial
classification of multiplicity-free Richardson varieties, i.e.,
we classify multiplicity-free products of Schubert classes. This answers
a question of W. Fulton.
| MSC Classifications: |
14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14M05 - Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10] 05E99 - None of the above, but in this section |