Realizability of some Böröoczky arrangements over the rational numbers

Janasz, Marek; Lampa-Baczyńska, Magdalena; Wójcik, Daniel

dc.contributor.author	Janasz, Marek
dc.contributor.author	Lampa-Baczyńska, Magdalena
dc.contributor.author	Wójcik, Daniel
dc.contributor.editor	Krasiński, Tadeusz
dc.contributor.editor	Spodzieja, Stanisław
dc.date.accessioned	2022-12-22T16:10:06Z
dc.date.available	2022-12-22T16:10:06Z
dc.date.issued	2022
dc.identifier.citation	Janasz M., Lampa-Baczyńska M., Wójcik D., Realizability of some Böröoczky arrangements over the rational numbers, [in:] Analitic and Algebraic Geometry 4, T. Krasiński, S. Spodzieja (ed.), WUŁ, Łódź 2022, https://doi.org/10.18778/8331-092-3.08	pl_PL
dc.identifier.isbn	978-83-8331-092-3
dc.identifier.uri	http://hdl.handle.net/11089/44832
dc.description.abstract	In this paper, we study the parameter spaces for Böröoczky arrangements Bn of n lines, where n < 12. We prove that up to n = 12, there exist only one arrangement nonrealizable over the rational numbers, that is B11.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	pl_PL
dc.relation.ispartof	Analitic and Algebraic Geometry 4;
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.title	Realizability of some Böröoczky arrangements over the rational numbers	pl_PL
dc.type	Book chapter	pl_PL
dc.page.number	83-93	pl_PL
dc.contributor.authorAffiliation	Uniwersytet Pedagogiczny w Krakowie, Instytut Matematyki	pl_PL
dc.contributor.authorAffiliation	Uniwersytet Pedagogiczny w Krakowie, Instytut Matematyki	pl_PL
dc.contributor.authorAffiliation	Uniwersytet Pedagogiczny w Krakowie, Instytut Matematyki	pl_PL
dc.identifier.eisbn	978-83-8331-093-0
dc.references	W. Bosma, J. Cannon, C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), no. 3–4, 235–265.	pl_PL
dc.references	D. W. Crowe, T. A. McKee, Sylvesters problem on collinear points, Math. Mag. 41 (1968), 30–34.	pl_PL
dc.references	A. Czapliński, A. Gówka-Habura, G. Malara, M. Lampa-Baczyńska, P. Łuszcz- Świdecka, P. Pokora and J. Szpond, A counterexample to the containment I(3) ⊂ I2 over the reals, Adv. Geom. 16 (2016) 77–82.	pl_PL
dc.references	W. Decker, G.-M. Greuel, G. Pfister, H. Sch¨onemann, H.: Singular 4-2-1 — A computer algebra system for polynomial computations. http://www.singular.uni-kl.de 2021.	pl_PL
dc.references	Ł. Farnik, J. Kabat, M. Lampa-Baczyńska and H. Tutaj-Gasińska, Containment problem and combinatorics, J. Algebraic Combin. 50 (2019), 39–47.	pl_PL
dc.references	Ł. Farnik, J. Kabat, M. Lampa-Baczyńska and H. Tutaj-Gasińska, On the parameter spaces of some B¨or¨oczky configurations, Int. J. of Algebra and Comput. 28 (2018), no. 7, 1231–1246.	pl_PL
dc.references	Z. F¨uredi, I. Pal´asti, Arrangements of lines with a large number of triangles, Proc. Amer. Math. Soc. 92 (1984), no. 4, 561–566.	pl_PL
dc.references	B. Green, T. Tao, On sets defining few ordinary lines, Discrete Comput. Geom. 50 (2013), 409–468.	pl_PL
dc.references	M. Lampa-Baczyńska, J. Szpond, From Pappus theorem to parameter spaces of some extremal line point configurations and applications, Geom. Dedicata 188 (2017) 103–121.	pl_PL
dc.references	B. Sturmfels, Computational algebraic geometry of projective configurations, J. Symbolic Computation 11 (1991), 595–618.	pl_PL
dc.contributor.authorEmail	marek.janasz@up.krakow.pl	pl_PL
dc.contributor.authorEmail	magdalena.lampa-baczynska@up.krakow.pl	pl_PL
dc.contributor.authorEmail	daniel.wojcik@up.krakow.pl	pl_PL
dc.identifier.doi	10.18778/8331-092-3.08