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Mathematics > Algebraic Geometry

arXiv:1812.10211 (math)
[Submitted on 26 Dec 2018 (v1), last revised 9 Dec 2019 (this version, v2)]

Title:Genus six curves, K3 surfaces, and stable pairs

Authors:J. Ross Goluboff
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Abstract:A general smooth curve of genus six lies on a quintic del Pezzo surface. In \cite{AK11}, Artebani and Kondō construct a birational period map for genus six curves by taking ramified double covers of del Pezzo surfaces. The map is not defined for special genus six curves. In this paper, we construct a smooth Deligne-Mumford stack $\mathfrak{P}_0$ parametrizing certain stable surface-curve pairs which essentially resolves this map. Moreover, we give an explicit description of pairs in $\mathfrak{P}_0$ containing special curves.
Comments: This is v2. Exposition has been improved due to referee comments. To appear in IMRN
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1812.10211 [math.AG]
  (or arXiv:1812.10211v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.10211

Submission history

From: J. Ross Goluboff [view email]
[v1] Wed, 26 Dec 2018 03:19:53 UTC (21 KB)
[v2] Mon, 9 Dec 2019 20:22:33 UTC (27 KB)
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