Maximally writhed real algebraic links
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DOI: 10.1007/s00222-018-0844-7
Abstract: Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots and links in $$\mathbb {RP}^3$$RP3 which is not a topological isotopy invariant. In this paper we study real algebraic links of degree d… read more here.
Keywords: writhed real; algebraic links; real algebraic; maximally writhed ... See more keywords
On Osculating Framing of Real Algebraic Links
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DOI: 10.1007/s40598-019-00120-z
Abstract: For a real algebraic link in $RP^3$, we prove that its encomplexed writhe (an invariant introduced by Viro) is maximal for a given degree and genus if and only if its self-linking number with respect… read more here.
Keywords: algebraic links; real algebraic; framing real; osculating framing ... See more keywords
Localization of real algebraic hypersurfaces with applications to the enumeration of the classes of relative equilibria of a (5 + 1)-body problem
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DOI: 10.1016/j.jmaa.2019.123813
Abstract: Abstract We extend classical results on the localization of zeros of real univariate polynomials to the localization of zero sets of real multivariate polynomials P, more precisely, of real algebraic hypersurfaces (assuming 0 is a… read more here.
Keywords: algebraic hypersurfaces; real algebraic; equilibria body; relative equilibria ... See more keywords
Variance of the volume of random real algebraic submanifolds
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DOI: 10.1090/tran/7478
Abstract: Let $\mathcal{X}$ be a complex projective manifold of dimension $n$ defined over the reals and let $M$ denote its real locus. We study the vanishing locus $Z\_{s\_d}$ in $M$ of a random real holomorphic section… read more here.
Keywords: algebraic submanifolds; volume; real algebraic; variance ... See more keywords