Conics associated with totally degenerate curves

Qixiao Ma

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arXiv · 1908.03170

Conics associated with totally degenerate curves

Qixiao Ma

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Abstract

Let $k$ be a field. Let $X/k$ be a stable curve whose geometric irreducible components are smooth rational curves. Taking Stein factorization of its normalization, we get a conic. We show the conic is non-split in certain cases. As an application, we show for $g\geq3$, the period and index of the universal genus $g$ curve both equal to $2g-2$.

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Qixiao Ma. 2019-08-08. Conics associated with totally degenerate curves. https://arxiv.org/abs/1908.03170

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