On resolving singularities of plane curves via a theorem attributed to Alfred Clebsch
Sign Up to like & getrecommendations! Published in 2021 at "Historia Mathematica"
DOI: 10.1016/j.hm.2021.02.001
Abstract: Abstract This paper discusses a theorem in birational geometry that J.L. Coolidge attributed to Alfred Clebsch. The background is reconstructed from letters Felix Klein exchanged with Max Noether in 1894, when Noether was completing work… read more here.
Keywords: alfred clebsch; singularities plane; attributed alfred; resolving singularities ... See more keywords
Generalized connected sum formula for the Arnold invariants of generic plane curves
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DOI: 10.1016/j.topol.2018.12.010
Abstract: Abstract We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants J ± and St behave under the generalized connected… read more here.
Keywords: generalized connected; sum formula; arnold invariants; plane curves ... See more keywords
ALEXANDER POLYNOMIALS OF COMPLEX PROJECTIVE PLANE CURVES
Sign Up to like & getrecommendations! Published in 2018 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972717001198
Abstract: We compute the Alexander polynomial of a nonreduced nonirreducible complex projective plane curve with mutually coprime orders of vanishing along its irreducible components in terms of certain multiplier ideals. read more here.
Keywords: projective plane; alexander polynomials; polynomials complex; plane curves ... See more keywords
TANGENT-FILLING PLANE CURVES OVER FINITE FIELDS
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DOI: 10.1017/s0004972723000382
Abstract: We study plane curves over finite fields whose tangent lines at smooth $\mathbb {F}_q$ -points together cover all the points of $\mathbb {P}^2(\mathbb {F}_q)$ . read more here.
Keywords: jats inline; plane curves; finite fields; inline formula ... See more keywords
Plane R-curves II
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DOI: 10.1080/00036811.2019.1600677
Abstract: ABSTRACT Let be the class of plane, oriented, rectifiable curves γ, such that, for almost every , the part of γ preceding x is outside the open disk of radius R, centered in , where… read more here.
Keywords: plane curves; plane;
Vortex Scattering of Monatomic Gas Along Plane Curves
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Applied Mechanics and Technical Physics"
DOI: 10.1134/s0021894418020074
Abstract: An invariant submodel of gas dynamics equations constructed on a three-dimensional subalgebra with a projective operator for the case of monatomic gas is under consideration. The submodel is reduced to an Abel equation, with integral… read more here.
Keywords: monatomic gas; vortex scattering; gas along; along plane ... See more keywords
GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves
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DOI: 10.1515/forum-2024-0043
Abstract: Abstract We study the quotient variety of the space of foliations on ℂ ℙ 2 {\mathbb{CP}^{2}} of degree 2 up to change of coordinates. We find the intersection Betti numbers of this variety. As… read more here.
Keywords: betti numbers; quartic plane; plane curves; foliations degree ... See more keywords