Algebraic geometry
Deformation of the product of complex Fano manifolds
Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 538-541.

Let X be a connected family of complex Fano manifolds. We show that if some fiber is the product of two manifolds of lower dimensions, then so is every fiber. Combining with previous work of Hwang and Mok, this implies immediately that if a fiber is a (possibly reducible) Hermitian symmetric space of compact type, then all fibers are isomorphic to the same variety.

Soit X une famille connexe des variétés de Fano complexes. On montre que, si une fibre est un produit de deux variétés de dimensions inférieures, alors il en est de même pour chaque fibre. En combinant avec un résultat de Hwang et Mok, ceci implique immédiatement que, si une fibre est un espace Hermitien symétrique de type compact, alors toutes les fibres sont isomorphes à cette variété.

Published online:
DOI: 10.1016/j.crma.2018.04.007
Li, Qifeng 1

1 Korea Institute for Advanced Study, Seoul, Republic of Korea
     author = {Li, Qifeng},
     title = {Deformation of the product of complex {Fano} manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {538--541},
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     year = {2018},
     doi = {10.1016/j.crma.2018.04.007},
     language = {en},
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Li, Qifeng. Deformation of the product of complex Fano manifolds. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 538-541. doi : 10.1016/j.crma.2018.04.007.

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