Bharali, Gautam and Biswas, Indranil (2014) RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES. In: INTERNATIONAL JOURNAL OF MATHEMATICS, 25 (1).
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In the study of holomorphic maps, the term ``rigidity'' refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin by studying when, given two compact connected complex manifolds X and Y, a degree-one holomorphic map f :Y -> X is a biholomorphism. Given that the real manifolds underlying X and Y are diffeomorphic, we provide a condition under which f is a biholomorphism. Using this result, we deduce a rigidity result for holomorphic self-maps of the total space of a holomorphic fiber space. Lastly, we consider products X = X-1 x X-2 and Y = Y-1 x Y-2 of compact connected complex manifolds. When X-1 is a Riemann surface of genus >= 2, we show that any non-constant holomorphic map F:Y -> X is of a special form.
| Item Type: | Journal Article |
|---|---|
| Publication: | INTERNATIONAL JOURNAL OF MATHEMATICS |
| Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD |
| Additional Information: | Copyright for this article belongs to the WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE |
| Keywords: | Degree-one maps; holomorphic fiber spaces; rigidity |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 04 Apr 2014 08:27 |
| Last Modified: | 04 Apr 2014 08:27 |
| URI: | http://eprints.iisc.ac.in/id/eprint/48769 |
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