A note on free determinantal hypersurface arrangements in P¹⁴C

Authors

  • Marek Janasz Pedagogical University of Krakow.
  • Paulina Wiśniewska Pedagogical University of Krakow.

DOI:

https://doi.org/10.22199/issn.0717-6279-5780

Keywords:

hypersurface arrangements, freeness, determinantal arrangements

Abstract

In the present note we study determinantal arrangements constructed with use of the 3-minors of a 3 × 5 generic matrix of indeterminates. In particular, we show that certain naturally constructed hypersurface arrangements in P14C are free.

Author Biographies

Marek Janasz, Pedagogical University of Krakow.

Department of Mathematics.

Paulina Wiśniewska, Pedagogical University of Krakow.

Department of Mathematics and Doctoral School.

References

R.-O. Buchweitz, D. Mond, Singularities and Computer Algebra. London Mathematical Society Lecture Note Series, vol. 324, pp. 41-77. Cambridge: Cambridge University Press, 2006.

L. Busé, A. Dimca, H. Schenck, and G. Sticlaru, “The Hessian polynomial and the Jacobian ideal of a reduced surface in Pn”, Advances in Mathematics, vol. 392, Article ID 108035, vol. 22, pp. 22, 2021. doi: 10.1016/j.aim.2021.108035

W. Decker, G.-M. Greuel, G. Pfister, and H. Schönemann, Singular 4-1-1 – A computer algebra system for polynomial computations, 2018. [On line]. Available: http://www.singular.uni-kl.de

A. Dimca, Hyperplane arrangements. An introduction. Universitext. Cham: Springer, 2017.

H. Schenck and S ̧. O. Tohăneanu, “Freeness of Conic-Line Arrangements in P2”, Commentarii Mathematici Helvetici, vol. 84, pp. 235-258, 2009.

A. Yim, “Homological properties of determinantal arrangements”, Journal of Algebra, vol. 471, pp. 220-239, 2017. https://doi.org/10.1016/j.jalgebra.2016.09.019

Published

2023-07-18

How to Cite

[1]
M. . Janasz and P. Wiśniewska, “A note on free determinantal hypersurface arrangements in P¹⁴C ”, Proyecciones (Antofagasta, On line), vol. 42, no. 4, pp. 1093-1104, Jul. 2023.

Issue

Section

Artículos