Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904722 | Advances in Mathematics | 2018 | 50 Pages |
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 â¥5 or an Inoue surface. We give examples of rigid manifolds of dimension nâ¥3 and Kodaira dimensions 0, and 2â¤kâ¤n. Our main theorem is that the Hirzebruch Kummer coverings of exponent nâ¥4 branched on a complete quadrangle are infinitesimally rigid. Moreover, we pose a number of questions.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Ingrid Bauer, Fabrizio Catanese,