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arXiv · 2501.02574

Multiple Lines of Maximum Genus in $\mathbb{P}^3$

Enrico Schlesinger
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Abstract

We introduce a notion of good cohomology for multiple lines in $\mathbb{P}^3$ and we classify multiple lines with good cohomology up to multiplicity 4. In particular, we show that the family of space curves of degree d, not lying on a surface of degree less than d, and of maximal arithmetic genus is not irreducible already for d=4 and d=5.

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Enrico Schlesinger. 2025-01-05. Multiple Lines of Maximum Genus in $\mathbb{P}^3$. https://doi.org/10.1007/s00009-024-02608-1

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