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RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES

Bharali, Gautam and Biswas, Indranil (2014) RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES. In: INTERNATIONAL JOURNAL OF MATHEMATICS, 25 (1).

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Official URL: http://dx.doi.org/10.1142/S0129167X14500062

Abstract

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
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
Depositing User: Id for Latest eprints
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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