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pro vyhledávání: '"Josse, Alfrederic"'
Autor:
Josse, Alfrederic, Pène, Françoise
The Halphen transform of a plane curve is the curve obtained by intersecting the tangent lines of the curve with the corresponding polar lines with respect to some conic. This transform has been introduced by Halphen as a branch desingularization met
Externí odkaz:
http://arxiv.org/abs/1506.08949
Autor:
Josse, Alfrederic, Pene, Francoise
We are interested in the normal class of an algebraic hypersurface Z of the complex projective space P^n, that is the number of normal lines to Z passing through a generic point of P^n. Thanks to the notion of normal polar, we state a formula for the
Externí odkaz:
http://arxiv.org/abs/1402.7266
Autor:
Josse, Alfrederic, Pene, Francoise
Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the reflected lines got by reflection of the incident lines (Sm) on Z at m in
Externí odkaz:
http://arxiv.org/abs/1304.3883
Autor:
Josse, Alfrederic, Pene, Francoise
We are interested in the study of caustics by reflection of irreducible algebraic planar curves (in the complex projective plane). We prove the birationality of the caustic map (for a generic light position). We also give simple formulas for the degr
Externí odkaz:
http://arxiv.org/abs/1301.1846
Autor:
Josse, Alfrederic, Pene, Francoise
Given any light position S in the complex projective plane P^2 and any algebraic curve C of P^2 (with any kind of singularities), we consider the incident lines coming from S (i.e. the lines containing S) and their reflected lines after reflection of
Externí odkaz:
http://arxiv.org/abs/1210.6551
Autor:
Josse, Alfrederic, Pene, Francoise
Given a point S and any irreducible algebraic curve C in P^2 (with any type of singularities), we consider the caustic of reflection defined as the Zariski closure of the envelope of the reflected lines from the point S on the curve C. We identify th
Externí odkaz:
http://arxiv.org/abs/1201.0621
Akademický článek
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Autor:
Josse, Alfrederic, Pene, Françoise
Given any light position S in the complex projective plane P^2 and any algebraic curve C of P^2 (with any kind of singularities), we consider the incident lines coming from S (i.e. the lines containing S) and their reflected lines after reflection of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::afe23a72cdc80fde4812b77551a07563
https://hal.archives-ouvertes.fr/hal-00744994v2/document
https://hal.archives-ouvertes.fr/hal-00744994v2/document
Akademický článek
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Autor:
Josse Alfrederic
Publikováno v:
Communications in Algebra. 23:4343-4364
We give a modern version of the following result of Halphen: “degrees and classes of successive evolutes of a plane algebraic curve form two arithmetic progressions of the same ratio after a sufficient number of iterations”. The iteration of this
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f568288b870b2693b1d7d264cc167aaf
https://doi.org/10.1080/00927879508825468
https://doi.org/10.1080/00927879508825468
