Optimal curve straightening to a target vertex count is ∃R-complete, and isotopy realization spaces of curves are universal up to homotopy equivalence.
Mnev-Sturmfels universality for schemes
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
cs.CG 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Optimal Curve Straightening is $\exists\mathbb{R}$-Complete
Optimal curve straightening to a target vertex count is ∃R-complete, and isotopy realization spaces of curves are universal up to homotopy equivalence.