LAUSR

On resolving singularities of plane curves via a theorem attributed to Alfred Clebsch

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1 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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0 Published in 2019 at "Topology and its Applications"

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

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0 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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1 Published in 2023 at "Bulletin of the Australian Mathematical Society"

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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0 Published in 2019 at "Applicable Analysis"

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

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1 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