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Mathematics > Algebraic Geometry

arXiv:2206.01235 (math)
[Submitted on 2 Jun 2022 (v1), last revised 8 Mar 2023 (this version, v2)]

Title:Duality for certain multi-Frobenius nonclassical curves in higher dimensional spaces

Authors:Nazar Arakelian
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Abstract:We show how a type of multi-Frobenius nonclassicality of a curve defined over a finite field $\mathbb{F}_q$ of characteristic $p$ reflects on the geometry of its strict dual curve. In particular, in such cases we may describe all the possible intersection multiplicities of its strict dual curve with the linear system of hyperplanes. Among other consequence, using a result by Homma, we are able to construct nonreflexive space curves such that their tangent surfaces are nonreflexive as well, and the image of a generic point by a Frobenius map is in its osculating hyperplane. We also obtain generalizations and improvements of some known results of the literature.
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:2206.01235 [math.AG]
  (or arXiv:2206.01235v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2206.01235

Submission history

From: Nazar Arakelian [view email]
[v1] Thu, 2 Jun 2022 18:21:01 UTC (17 KB)
[v2] Wed, 8 Mar 2023 17:47:16 UTC (18 KB)
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