Elliptic curves on spinor varieties
Tóm tắt
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.
Tài liệu tham khảo
Atiyah M.F., Vector bundles over an elliptic curve, Proc. London Math. Soc., 1957, 7, 414–452
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
Bourbaki N., Éléments de Mathématique. XXVI. Groupes et Algèbres de Lie. Chapitre 1: Algèbres de Lie, Actualités Sci. Ind., 1285, Hermann, Paris, 1960
Brion M., Kumar S., Frobenius Splitting Methods in Geometry and Representation Theory, Progr. Math., 231, Birkhäuser, Boston, 2005
Bruguières A., The scheme of morphisms from an elliptic curve to a Grassmannian, Compositio Math., 1987, 63(1), 15–40
Chaput P.E., Manivel L., Perrin N., Quantum cohomology of minuscule homogeneous spaces, Transform. Groups, 2008, 13(1), 47–89
Demazure M., Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup., 1974, 7(1), 53–88
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
Kleiman S.L., The transversality of a general translate, Compositio Math., 1974, 28, 287–297
Magyar P., Schubert polynomials and Bott-Samelson varieties, Comment. Math. Helv., 1998, 73(4), 603–636
Pasquier B., Perrin N., Elliptic curves on some homogeneous spaces, preprint available at http://arxiv.org/abs/1105.5320
Perrin N., Courbes rationnelles sur les variétés homogènes, Ann. Inst. Fourier (Grenoble), 2002, 52(1), 105–132
Perrin N., Rational curves on minuscule Schubert varieties, J. Algebra, 2005, 294(2), 431–462
Perrin N., Small resolutions of minuscule Schubert varieties, Compos. Math., 2007, 143(5), 1255–1312
Stembridge J.R., Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc., 1997, 349(4), 1285–1332