Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ arXiv.org e-Print Ar...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
arXiv.org e-Print Archive
Other literature type . Preprint . 2020
https://doi.org/10.48550/arxiv...
Article . 2020
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
versions View all 3 versions
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

A bound for the number of points of space curves over finite fields

Authors: Beelen, Peter; Montanucci, Maria;

A bound for the number of points of space curves over finite fields

Abstract

For a non-degenerate irreducible curve $C$ of degree $d$ in $\mathbb{P}^3$ over $\mathbb{F}_q$, we prove that the number $N_q(C)$ of $\mathbb{F}_q$-rational points of $C$ satisfies the inequality $N_q(C) \leq (d-2)q+1$. Our result improves the previous bound $N_q(C) \leq (d-1)q+1$ obtained by Homma in 2012 and leads to a natural conjecture generalizing Sziklai's bound for the number of points of plane curves over finite fields.

Keywords

Mathematics - Algebraic Geometry, FOS: Mathematics, Algebraic Geometry (math.AG)

12 references, page 1 of 2

i(π ∩ C, P ) ≥ 4.

[1] E. Ballico, Special inner projections of projective varieties, Ann. Univ. Ferrara 50, 23-26 (2004). [OpenAIRE]

[2] V. Bayer and A. Hefez, Strange curves, Comm. Algebra 19, 3041-3059 (1991). [OpenAIRE]

[3] R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52. Springer-Verlag, New YorkHeidelberg, (1977).

[4] J.W.P. Hirschfeld, G. Korchm´aros and F. Torres, Algebraic Curves over a Finite Field, Princeton Series in Applied Mathematics, Princeton, (2008).

[5] M. Homma, A bound on the number of points of a curve in projective space over a finite field, Theory and Applications of Finite Fields in: Contemp. Mat. 579, 103-110 (2012).

[6] M. Homma and S.J. Kim, Around Sziklai's conjecture on the number of points of a plane curve over a finite field, Finite Fields and Appl. 15, 468-474 (2009). [OpenAIRE]

[7] M. Homma and S.J. Kim, Sziklai's conjecture on the number of points of a plane curve over a finite field II, in: G. McGuire, G.L. Mullen, D. Panario, I.E. Shparlinski (Eds.), Finite Fields: Theory and Applications, in: Contemp. Math. 518, AMS, Providence, 225-234 (2010).

[8] M. Homma and S.J. Kim, Sziklai's conjecture on the number of points of a plane curve over a finite field III, Finite Fields and Appl. 16, 315-319 (2010). [OpenAIRE]

[9] P. Samuel, Lectures on old and new results on algebraic curves (notes by Anantharaman), Tata Inst. Fund. Res., (1966).

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
  • citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
    Powered byBIP!BIP!
Powered by OpenAIRE graph
Found an issue? Give us feedback
citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green