Rank two vector bundles on polarised Halphen surfaces and the Gauss-Wahl map for du Val curves

Enrico Arbarello; Andrea Bruno

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arXiv · 1609.09256

Rank two vector bundles on polarised Halphen surfaces and the Gauss-Wahl map for du Val curves

Enrico Arbarello·Andrea Bruno

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Abstract

A genus-g du Val curve is a degree-3g plane curve having 8 points of multiplicity g, one point of multiplicity g-1, and no other singularity. We prove that the corank of the Gauss-Wahl map of a general du Val curve of odd genus (>11) is equal to one. This, together with the results of [1], shows that the characterisation of Brill-Noether-Petri curves with non-surjective Gauss-Wahl map as hyperplane sections of K3 surfaces and limits thereof, obtained in [3], is optimal.

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Enrico Arbarello, Andrea Bruno. 2016-09-29. Rank two vector bundles on polarised Halphen surfaces and the Gauss-Wahl map for du Val curves. https://arxiv.org/abs/1609.09256

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