UZH-Logo

Maintenance Infos

Quantum cohomology of orthogonal Grassmannians


Kresch, A; Tamvakis, H (2004). Quantum cohomology of orthogonal Grassmannians. Compositio Mathematica, 140(2):482-500.

Abstract

Let V be a vector space with a non-degenerate symmetric form and OG be the
orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give
a presentation for the (small) quantum cohomology ring QH ∗ (OG) and show that
its product structure is determined by the ring of P˜-polynomials. A 'quantum Schubert
calculus' is formulated, which includes quantum Pieri and Giambelli formulas, as well as
algorithms for computing Gromov–Witten invariants. As an application, we show that the
table of three-point, genus zero Gromov–Witten invariants for OG coincides with that for
a corresponding Lagrangian Grassmannian LG, up to an involution.

Let V be a vector space with a non-degenerate symmetric form and OG be the
orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V . We give
a presentation for the (small) quantum cohomology ring QH ∗ (OG) and show that
its product structure is determined by the ring of P˜-polynomials. A 'quantum Schubert
calculus' is formulated, which includes quantum Pieri and Giambelli formulas, as well as
algorithms for computing Gromov–Witten invariants. As an application, we show that the
table of three-point, genus zero Gromov–Witten invariants for OG coincides with that for
a corresponding Lagrangian Grassmannian LG, up to an involution.

Citations

21 citations in Web of Science®
21 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

29 downloads since deposited on 29 Nov 2010
10 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:quot schemes; Schubert calculus
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:London Mathematical Society
ISSN:0010-437X
Additional Information:© Foundation Compositio Mathematica 2004.
Publisher DOI:10.1112/S0010437X03000204
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2027200
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1077.14083
Permanent URL: http://doi.org/10.5167/uzh-21809

Download

[img]
Preview
Filetype: PDF (Preprint)
Size: 386kB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations