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Mnev-Sturmfels universality for schemes

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arxiv 1202.3934 v2 pith:F4MKXN63 submitted 2012-02-17 math.AG

Seok Hyeong Lee , Ravi Vakil This is my paper · ORCID
classification math.AG
keywords mnev-sturmfelssometypeuniversalityalgebraicappearsconstraintsfinite
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We prove a scheme-theoretic version of Mnev-Sturmfels Universality, suitable to be used in the proof of Murphy's Law in Algebraic Geometry. Somewhat more precisely, we show that any singularity type of finite type over Z appears on some incidence scheme of points and lines, subject to some particular further constraints.

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  1. Optimal Curve Straightening is $\exists\mathbb{R}$-Complete

    cs.CG 2019-08 conditional novelty 6.0 of 10

    Optimal curve straightening to a target vertex count is ∃R-complete, and isotopy realization spaces of curves are universal up to homotopy equivalence.

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