Projected Gromov-Witten varieties in cominuscule spaces
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- by Anders S. Buch, Pierre–Emmanuel Chaput, Leonardo C. Mihalcea and Nicolas Perrin PDF
- Proc. Amer. Math. Soc. 146 (2018), 3647-3660 Request permission
Abstract:
A projected Gromov-Witten variety is the union of all rational curves of fixed degree that meet two opposite Schubert varieties in a homogeneous space $X = G/P$. When $X$ is cominuscule we prove that the map from a related Gromov-Witten variety is cohomologically trivial. This implies that all (3-point, genus zero) $K$-theoretic Gromov-Witten invariants of $X$ are determined by projected Gromov-Witten varieties, which extends an earlier result of Knutson, Lam, and Speyer, and provides an alternative version of the ‘quantum equals classical’ theorem. Our proof uses that any projected Gromov-Witten variety in a cominuscule space is also a projected Richardson variety.References
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Additional Information
- Anders S. Buch
- Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854
- MR Author ID: 607314
- Email: asbuch@math.rutgers.edu
- Pierre–Emmanuel Chaput
- Affiliation: Domaine Scientifique Victor Grignard, 239, Boulevard des Aiguillettes, Université de Lorraine, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy Cedex, France
- Email: pierre-emmanuel.chaput@univ-lorraine.fr
- Leonardo C. Mihalcea
- Affiliation: Department of Mathematics, Virginia Tech University, 460 McBryde Street, Blacksburg, Virginia 24060
- Email: lmihalce@math.vt.edu
- Nicolas Perrin
- Affiliation: Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035 Versailles, France
- MR Author ID: 661087
- Email: nicolas.perrin@uvsq.fr
- Received by editor(s): January 9, 2015
- Received by editor(s) in revised form: May 5, 2017
- Published electronically: May 15, 2018
- Additional Notes: The first author was supported in part by NSF grant DMS-1205351.
The third author was supported in part by NSA Awards H98230-13-1-0208 and H98320-16-1-0013 and a Simons Collaboration Grant.
The fourth author was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH. - Communicated by: Lev Borisov
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3647-3660
- MSC (2010): Primary 14N35; Secondary 19E08, 14N15, 14M15, 14M20, 14M22
- DOI: https://doi.org/10.1090/proc/13839
- MathSciNet review: 3825822