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arXiv · 1306.0787

On the surjectivity of weighted Gaussian maps

Edoardo Ballico·Letizia Pernigotti
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Abstract

We study the surjectivity of suitable weighted Gaussian maps which provide a natural generalization of the standard Gaussian maps and encode the local geometry of the locus of curves endowed with a higher root of the canonical bundle having associated linear system of dimension at least r + 1. In particular, we get a bound on the dimension of its Zariski tangent space, which turns out to be sharp in the special case r = 0. Finally, we describe this locus in the case of complete intersection curves.

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Edoardo Ballico, Letizia Pernigotti. 2013-06-04. On the surjectivity of weighted Gaussian maps. https://arxiv.org/abs/1306.0787

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