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arXiv · 1402.1108

Extrinsic projective curves X^1 in P^2(C): harmony with intrinsic cohomology

Joel Merker
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Abstract

On a geometrically smooth complex algebraic curve X^1 in P^2(C), represented in complex affine coordinates (x,y) as the zero-locus R(x,y) = 0 of some polynomial R of degree d >= k+3, an explicit family of generating independent holomorphic jet differentials J_R^1, ..., J_R^k expressed in terms of R and its partial derivatives is exhibited with its new precious nonlinearity features as a complete explicitation of all holomorphic sections of the Green-Griffiths bundle of m-homogeneous polynomialized order k jets of local holomorphic maps from a complex disc into X^1.

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Joel Merker. 2014-02-05. Extrinsic projective curves X^1 in P^2(C): harmony with intrinsic cohomology. https://arxiv.org/abs/1402.1108

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