On rigid compact complex surfaces and manifolds
This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the relations among them. Only for curves these notions coincide a...
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| Published in | Advances in mathematics (New York. 1965) Vol. 333; pp. 620 - 669 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
31.07.2018
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| ISSN | 0001-8708 1090-2082 1090-2082 |
| DOI | 10.1016/j.aim.2018.05.041 |
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| Abstract | This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the relations among them. Only for curves these notions coincide and the only rigid curve is the projective line. For surfaces we prove that a rigid surface which is not minimal of general type is either a Del Pezzo surface of degree ≥5 or an Inoue surface. We give examples of rigid manifolds of dimension n≥3 and Kodaira dimensions 0, and 2≤k≤n. Our main theorem is that the Hirzebruch Kummer coverings of exponent n≥4 branched on a complete quadrangle are infinitesimally rigid. Moreover, we pose a number of questions. |
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| AbstractList | This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the relations among them. Only for curves these notions coincide and the only rigid curve is the projective line. For surfaces we prove that a rigid surface which is not minimal of general type is either a Del Pezzo surface of degree ≥5 or an Inoue surface. We give examples of rigid manifolds of dimension n≥3 and Kodaira dimensions 0, and 2≤k≤n. Our main theorem is that the Hirzebruch Kummer coverings of exponent n≥4 branched on a complete quadrangle are infinitesimally rigid. Moreover, we pose a number of questions. |
| Author | Bauer, Ingrid Catanese, Fabrizio |
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| Keywords | 14J15 14F17 14D07 14J29 Deformation theory Projective classifying spaces 32J15 Rigid complex manifolds 14B12 14E20 32G05 14J80 32Q55 Branched or unramified coverings |
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| Title | On rigid compact complex surfaces and manifolds |
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