Displaying similar documents to “Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1”

Extension of holomorphic maps between real hypersurfaces of different dimension

Rasul Shafikov, Kausha Verma (2007)

Annales de l’institut Fourier

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In this paper we extend the results on analytic continuation of germs of holomorphic mappings from a real analytic hypersurface to a real algebraic hypersurface to the case when the target hypersurface is of higher dimension than the source. More precisely, we prove the following: Let M be a connected smooth real analytic minimal hypersurface in C n , M be a compact strictly pseudoconvex real algebraic hypersurface in C N , 1 < n N . Suppose that f is a germ of a holomorphic map at a point p in M ...

On the embedding and compactification of q -complete manifolds

Ionuţ Chiose (2006)

Annales de l’institut Fourier

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We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form N N - q . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as X ¯ ( X ¯ N - q ) where X ¯ N is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into 1 × N .

On fundamental groups of algebraic varieties and value distribution theory

Katsutoshi Yamanoi (2010)

Annales de l’institut Fourier

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If a smooth projective variety X admits a non-degenerate holomorphic map X from the complex plane , then for any finite dimensional linear representation of the fundamental group of X the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.

Uniqueness in Rough Almost Complex Structures, and Differential Inequalities

Jean-Pierre Rosay (2010)

Annales de l’institut Fourier

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The study of J -holomorphic maps leads to the consideration of the inequations | u z ¯ | C | u | , and | u z ¯ | ϵ | u z | . The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of u vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class 1 2 , any J -holomorphic curve that is constant on...

Obstructions to deforming curves on a 3 -fold, II: Deformations of degenerate curves on a del Pezzo 3 -fold

Hirokazu Nasu (2010)

Annales de l’institut Fourier

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We study the Hilbert scheme Hilb s c V of smooth connected curves on a smooth del Pezzo 3 -fold V . We prove that any degenerate curve C , any curve C contained in a smooth hyperplane section S of V , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) χ ( V , C ( S ) ) 1 and (ii) for every line on S such that C = , the normal bundle N / V is trivial (  N / V 𝒪 1 2 ). As a consequence, we prove an analogue (for Hilb s c V ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...