RIGIDITY OF HOLOMORPHIC MAPS BETWEEN FIBER SPACES

Content Provider	Indian Institute of Science (IISc)
Author	Bharali, Gautam Biswas, Indranil
Copyright Year	2014
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.
File Format	PDF
Journal	PeerReviewed
Language	English
Publisher	WORLD SCIENTIFIC PUBL CO PTE LTD
Publisher Date	2014-01-01
Access Restriction	Authorized
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article