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Article Dans Une Revue Le Matematiche Année : 2022

Computing totally real hyperplane sections and linear series on algebraic curves

Résumé

Given a real algebraic curve, embedded in projective space, we study the computational problem of deciding whether there exists a hyperplane meeting the curve in real points only. More generally, given any divisor on such a curve, we may ask whether the corresponding linear series contains an effective divisor with totally real support. This translates into a particular type of parametrized real root counting problem that we wish to solve exactly. On the other hand, it is known that for a given genus and number of real connected components, any linear series of sufficiently large degree contains a totally real effective divisor. Using the algorithms described in this paper, we solve a number of examples, which we can compare to the best known bounds for the required degree.
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Dates et versions

hal-03283378 , version 1 (10-07-2021)
hal-03283378 , version 2 (25-11-2021)

Identifiants

Citer

Huu Phuoc Le, Dimitri Manevich, Daniel Plaumann. Computing totally real hyperplane sections and linear series on algebraic curves. Le Matematiche, 2022, 77 (1), pp.119-141. ⟨10.4418/2022.77.1.7⟩. ⟨hal-03283378v2⟩
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