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arXiv · 1712.05710

Quintic threefolds with triple points

Remke Kloosterman·Slawomir Rams
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Abstract

We study the geometry of quintic threefolds $X\subset \mathbb{P}^4$ with only ordinary triple points as singularities. In particular, we show that if a quintic threefold $X$ has a reducible hyperplane section then $X$ has at most $10$ ordinary triple points, and that this bound is sharp. We construct various examples of quintic threefolds with triple points and discuss their defect.

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Remke Kloosterman, Slawomir Rams. 2017-12-15. Quintic threefolds with triple points. https://doi.org/10.1142/s0219199719500858

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