[Sur la rigidité de la déformation de variétés projectives lisses symétriques de nombre de Picard un]
Les variétés symétriques sont les plongements ouverts normaux équivariants des espaces homogènes symétriques et ce sont des exemples intéressants de variétés sphériques. L'objectif principal de cet article est d'étudier la rigidité sous les déformations kähleriennes des variétés projectives lisses symétriques de nombre de Picard un.
Symmetric varieties are normal equivariant open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. The principal goal of this article is to study the rigidity under Kähler deformations of smooth projective symmetric varieties with Picard number one.
Accepté le :
Publié le :
@article{CRMATH_2019__357_11-12_889_0,
author = {Shin-Young Kim and Kyeong-Dong Park},
title = {On the deformation rigidity of smooth projective symmetric varieties with {Picard} number one},
journal = {Comptes Rendus. Math\'ematique},
pages = {889--896},
publisher = {Elsevier},
volume = {357},
number = {11-12},
year = {2019},
doi = {10.1016/j.crma.2019.10.008},
language = {en},
}
TY - JOUR AU - Shin-Young Kim AU - Kyeong-Dong Park TI - On the deformation rigidity of smooth projective symmetric varieties with Picard number one JO - Comptes Rendus. Mathématique PY - 2019 SP - 889 EP - 896 VL - 357 IS - 11-12 PB - Elsevier DO - 10.1016/j.crma.2019.10.008 LA - en ID - CRMATH_2019__357_11-12_889_0 ER -
Shin-Young Kim; Kyeong-Dong Park. On the deformation rigidity of smooth projective symmetric varieties with Picard number one. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 889-896. doi : 10.1016/j.crma.2019.10.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.10.008/
[1] On Fano complete intersections in rational homogeneous varieties, Math. Z. (2019) (in press) | DOI
[2] Homogeneous vector bundles, Ann. of Math. (2), Volume 66 (1957) no. 2, pp. 203-248
[3] Lie groups in the foundations of geometry, Adv. Math., Volume 1 (1964) no. 2, pp. 145-190
[4] Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity, Invent. Math., Volume 189 (2012) no. 2, pp. 457-513
[5] Special birational transformations of type (2, 1), J. Algebraic Geom., Volume 27 (2018) no. 1, pp. 55-89
[6] Isotrivial VMRT-structures of complete intersection type, Asian J. Math., Volume 22 (2018) no. 2, pp. 0333-0354
[7] Geometry of minimal rational curves on Fano manifolds, school on vanishing theorems and effective results, Trieste, 2000 (ICTP Lect. Notes), Volume vol. 6, Abdus Salam Int. Cent. Theoret. Phys., Trieste (2001), pp. 335-393
[8] Characterizing symplectic Grassmannians by varieties of minimal rational tangents, 2019 (preprint) | arXiv
[9] Rigidity of irreducible Hermitian symmetric spaces of the compact type under Kähler deformation, Invent. Math., Volume 131 (1998) no. 2, pp. 393-418
[10] Varieties of minimal rational tangents on uniruled projective manifolds, Several Complex Variables (Berkeley, CA, 1995–1996), Math. Sci. Res. Inst. Publ., 37, Cambridge University Press, Cambridge, UK, 1999, pp. 351-389
[11] Deformation rigidity of the rational homogeneous space associated to a long simple root, Ann. Sci. Éc. Norm. Supér., Volume 35 (2002) no. 2, pp. 173-184
[12] Deformation rigidity of the 20-dimensional -homogeneous space associated to a short root, Algebraic Transformation Groups and Algebraic Varieties, Encyclopaedia of Mathematical Sciences, vol. 132, Springer, Berlin, 2004, pp. 37-58
[13] Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation, Invent. Math., Volume 160 (2005) no. 3, pp. 591-645
[14] Families of singular rational curves, J. Algebraic Geom., Volume 11 (2002) no. 2, pp. 245-256
[15] Complex Manifolds and Deformation of Complex Structures, Grundlehren der Mathematischen Wissenschaften, vol. 283, Springer, Berlin-Heidelberg-New York, 1986
[16] The projective geometry of Freudenthal's magic square, J. Algebra, Volume 239 (2001) no. 2, pp. 477-512
[17] Representation theory and projective geometry, Algebraic Transformation Groups and Algebraic Varieties, Encyclopaedia of Mathematical Sciences, vol. 132, Springer, Berlin, 2004, pp. 71-122
[18] The Cayley Grassmannian, J. Algebra, Volume 503 (2018), pp. 277-298
[19] L. Manivel, The double Cayley Grassmannian, in preparation.
[20] Deformation rigidity of odd Lagrangian Grassmannians, J. Korean Math. Soc., Volume 53 (2016) no. 3, pp. 489-501
[21] Geometrical description of smooth projective symmetric varieties with Picard number one, Transform. Groups, Volume 15 (2010) no. 1, pp. 201-226
[22] Smooth projective symmetric varieties with Picard number one, Int. J. Math., Volume 22 (2011) no. 2, pp. 145-177
[23] Opération de groupes réductifs dans un type de cônes presque homogènes, Bull. Soc. Math. Fr., Volume 102 (1974), pp. 317-334
[24] Cohomology of Vector Bundles and Syzygies, Cambridge Tracks in Mathematics, vol. 149, Cambridge University Press, 2003
[25] Tangents and Secants of Algebraic Varieties, Translations of Mathematical Monographs, vol. 127, American Mathematical Society, Providence, RI, USA, 1993
Cité par Sources :
Commentaires - Politique
Equivariant compactifications of vector groups with high index
Baohua Fu; Pedro Montero
C. R. Math (2019)