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2005•Journal of the Mathematical Society of JapanOpen access

Deficiencies of meromorphic mappings for hypersurfaces

Yoshihiro Aihara, Seiki Mori

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Abstract

In this paper we first prove that, for every hypersurface D of degree d in a complex projective space, there exists a holomorphic curve f from the complex plane into the projective space whose deficiency for D is positive and less than one. Using this result, we construct meromorphic mappings from the complex m -space into the complex projective space with the same properties. We also investigate the effect of resolution of singularities to defects of meromorphic mappings.

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What this paper is about

In this paper we first prove that, for every hypersurface D of degree d in a complex projective space, there exists a holomorphic curve f from the complex plane into the projective space whose deficiency for D is positive and less than one. Using this result, we construct meromorphic mappings from the complex m -space into the complex projective space with the same properties. We also investigate the effect of resolution of singularities to defects of meromorphic mappings.

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Available abstract

In this paper we first prove that, for every hypersurface D of degree d in a complex projective space, there exists a holomorphic curve f from the complex plane into the projective space whose deficiency for D is positive and less than one. Using this result, we construct meromorphic mappings from the complex m -space into the complex projective space with the same properties. We also investigate the effect of resolution of singularities to defects of meromorphic mappings.

Key concepts: Meromorphic function, Hypersurface, Mathematics, Holomorphic function, Complex projective space, Complex space, Projective space, Pure mathematics

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