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On Surjective Quadratic Maps of \(\boldsymbol{\mathbb{P}}^{\mathbf{2}}\)

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Abstract

In this article we give the criterion of surjectivity of quadratic maps in the case of \({\mathbb{P}}^{2}\). Using this criterion, we prove that surjective quadratic maps form a Zariski-open subset in the space of dominant quadratic maps of \({\mathbb{P}}^{2}\).

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ACKNOWLEDGMENTS

We are very grateful to Ilya Karzhemanov for very fruitful discussions and support.

Funding

This work is supported by the Russian Science Foundation under grant 23-21-00345, https://rscf.ru/project/23-21-00345/.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Laboratory of Algebraic Geometry and Homological Algebra, 141701, Dolgoprudny, Moscow oblast, Russia

    A. A. Kulikov & I. Yu. Zhdanovskiy

Authors
  1. A. A. Kulikov
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  2. I. Yu. Zhdanovskiy
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Corresponding authors

Correspondence to A. A. Kulikov or I. Yu. Zhdanovskiy.

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(Submitted by G. G. Amosov)

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Kulikov, A.A., Zhdanovskiy, I.Y. On Surjective Quadratic Maps of \(\boldsymbol{\mathbb{P}}^{\mathbf{2}}\). Lobachevskii J Math 44, 2072–2078 (2023). https://doi.org/10.1134/S1995080223060264

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  • DOI: https://doi.org/10.1134/S1995080223060264

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