Elliptic curves on spinor varieties
Open Mathematics (2012)
- Volume: 10, Issue: 4, page 1393-1406
- ISSN: 2391-5455
Access Full Article
top
Abstract
topHow to cite
topNicolas Perrin. "Elliptic curves on spinor varieties." Open Mathematics 10.4 (2012): 1393-1406. <http://eudml.org/doc/269650>.
@article{NicolasPerrin2012,
abstract = {We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.},
author = {Nicolas Perrin},
journal = {Open Mathematics},
keywords = {Elliptic curve; Spinor variety; spinor variety; orthogonal Grassmannian; elliptic curve; quantum cohomology; Chow group},
language = {eng},
number = {4},
pages = {1393-1406},
title = {Elliptic curves on spinor varieties},
url = {http://eudml.org/doc/269650},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Nicolas Perrin
TI - Elliptic curves on spinor varieties
JO - Open Mathematics
PY - 2012
VL - 10
IS - 4
SP - 1393
EP - 1406
AB - We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
LA - eng
KW - Elliptic curve; Spinor variety; spinor variety; orthogonal Grassmannian; elliptic curve; quantum cohomology; Chow group
UR - http://eudml.org/doc/269650
ER -
References
top- [1] Atiyah M.F., Vector bundles over an elliptic curve, Proc. London Math. Soc., 1957, 7, 414–452 http://dx.doi.org/10.1112/plms/s3-7.1.414 Zbl0084.17305
- [2] Ballico E., On the Hilbert scheme of curves in a smooth quadric, In: Deformations of Mathematical Structures, Łódz/Lublin, 1985/87, Kluwer, Dordrecht, 1989, 127–132 http://dx.doi.org/10.1007/978-94-009-2643-1_11
- [3] Bourbaki N., Éléments de Mathématique. XXVI. Groupes et Algèbres de Lie. Chapitre 1: Algèbres de Lie, Actualités Sci. Ind., 1285, Hermann, Paris, 1960
- [4] Brion M., Kumar S., Frobenius Splitting Methods in Geometry and Representation Theory, Progr. Math., 231, Birkhäuser, Boston, 2005 Zbl1072.14066
- [5] Bruguières A., The scheme of morphisms from an elliptic curve to a Grassmannian, Compositio Math., 1987, 63(1), 15–40 Zbl0664.14005
- [6] Chaput P.E., Manivel L., Perrin N., Quantum cohomology of minuscule homogeneous spaces, Transform. Groups, 2008, 13(1), 47–89 http://dx.doi.org/10.1007/s00031-008-9001-5 Zbl1147.14023
- [7] Demazure M., Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup., 1974, 7(1), 53–88 Zbl0312.14009
- [8] Iliev A., Markushevich D., Parametrization of sing Θ for a Fano 3-fold of genus 7 by moduli of vector bundles, Asian J. Math., 2007, 11(3), 427–458 Zbl1136.14031
- [9] Kleiman S.L., The transversality of a general translate, Compositio Math., 1974, 28, 287–297 Zbl0288.14014
- [10] Magyar P., Schubert polynomials and Bott-Samelson varieties, Comment. Math. Helv., 1998, 73(4), 603–636 http://dx.doi.org/10.1007/s000140050071 Zbl0951.14036
- [11] Pasquier B., Perrin N., Elliptic curves on some homogeneous spaces, preprint available at http://arxiv.org/abs/1105.5320
- [12] Perrin N., Courbes rationnelles sur les variétés homogènes, Ann. Inst. Fourier (Grenoble), 2002, 52(1), 105–132 http://dx.doi.org/10.5802/aif.1878
- [13] Perrin N., Rational curves on minuscule Schubert varieties, J. Algebra, 2005, 294(2), 431–462 http://dx.doi.org/10.1016/j.jalgebra.2005.08.031 Zbl1093.14070
- [14] Perrin N., Small resolutions of minuscule Schubert varieties, Compos. Math., 2007, 143(5), 1255–1312 http://dx.doi.org/10.1112/S0010437X07002734 Zbl1129.14069
- [15] Stembridge J.R., Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc., 1997, 349(4), 1285–1332 http://dx.doi.org/10.1090/S0002-9947-97-01805-9 Zbl0945.05064
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.