A few introductory remarks on line arrangements

Szpond, Justyna

dc.contributor.author	Szpond, Justyna
dc.contributor.editor	Krasiński, Tadeusz
dc.contributor.editor	Spodzieja, Stanisław
dc.date.accessioned	2020-01-28T12:29:17Z
dc.date.available	2020-01-28T12:29:17Z
dc.date.issued	2019
dc.identifier.citation	Szpond J., A few introductory remarks on line arrangements, in: Analytic and Algebraic Geometry 3, T. Krasiński, S. Spodzieja (red.), WUŁ, Łódź 2019, doi: 10.18778/8142-814-9.15.	pl_PL
dc.identifier.isbn	978-83-8142-814-9
dc.identifier.uri	http://hdl.handle.net/11089/31346
dc.description.abstract	Points and lines can be regarded as the simplest geometrical objects. Incidence relations between them have been studied since ancient times. Strangely enough our knowledge of this area of mathematics is still far from being complete. In fact a number of interesting and apparently difficult conjectures has been raised just recently. Additionally a number of interesting connections to other branches of mathematics have been established. This is an attempt to record some of these recent developments.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	pl_PL
dc.relation.ispartof	Analytic and Algebraic Geometry 3;
dc.rights	Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.title	A few introductory remarks on line arrangements	pl_PL
dc.type	Book chapter	pl_PL
dc.page.number	201-212	pl_PL
dc.contributor.authorAffiliation	Pedagogical University of Cracow, Department of Mathematics	pl_PL
dc.identifier.eisbn	978-83-8142-815-6
dc.references	M. Aigner and G. M. Ziegler. Proofs from The Book. Springer, Berlin, sixth edition, 2018. See corrected reprint of the 1998 original [ MR1723092], Including illustrations by Karl H. Hofmann.	pl_PL
dc.references	M. Artebani and I. Dolgachev. The Hesse pencil of plane cubic curves. Enseign. Math. (2), 55(3-4):235-273, 2009.	pl_PL
dc.references	T. Bauer, S. Di Rocco, B. Harbourne, J. Huizenga, A. Lundman, P. Pokora, and T. Szemberg. Bounded negativity and arrangements of lines. Int. Math. Res. Not. IMRN, (19):9456{9471, 2015.	pl_PL
dc.references	T. Bauer, G. Malara, T. Szemberg, and J. Szpond. Quartic unexpected curves and surfaces. Manuscripta Math., to appear, doi.org/10.1007/s00229-018-1091-3.	pl_PL
dc.references	C. Bocci and B. Harbourne. Comparing powers and symbolic powers of ideals. J. Algebraic Geom., 19(3):399-417, 2010.	pl_PL
dc.references	C. Bocci and B. Harbourne. The resurgence of ideals of points and the containment problem. Proc. Amer. Math. Soc., 138(4):1175-1190, 2010.	pl_PL
dc.references	D. Cook II, B. Harbourne, J. Migliore, and U. Nagel. Line arrangements and con gurations of points with an unexpected geometric property. Compos. Math., 154(10):2150-2194, 2018.	pl_PL
dc.references	H. S. M. Coxeter. A problem of collinear points. Amer. Math. Monthly, 55:26-28, 1948.	pl_PL
dc.references	D. W. Crowe and T. A. McKee. Sylvester's problem on collinear points. Math. Mag., 41:30- 34, 1968.	pl_PL
dc.references	J. Csima and E. T. Sawyer. There exist 6n=13 ordinary points. Discrete Comput. Geom., 9(2):187-202, 1993.	pl_PL
dc.references	A. Czapliński, A. Główka, G. Malara, M. Lampa-Baczyńska, P. Luszcz-Świdecka, P. Pokora, and J. Szpond. A counterexample to the containment I(3) I2 over the reals. Adv. Geom., 16(1):77-82, 2016.	pl_PL
dc.references	N. G. de Bruijn and P. Erd os. On a combinatorial problem. Nederl. Akad. Wetensch., Proc., 51:1277{1279 = Indagationes Math. 10, 421-423 (1948), 1948.	pl_PL
dc.references	R. Di Gennaro, G. Ilardi, and J. Vall es. Singular hypersurfaces characterizing the Lefschetz properties. J. Lond. Math. Soc. (2), 89(1):194-212, 2014.	pl_PL
dc.references	M. Dumnicki, B. Harbourne, U. Nagel, A. Seceleanu, T. Szemberg, and H. Tutaj-Gasińska. Resurgences for ideals of special point con gurations in PN coming from hyperplane arrangements. J. Algebra, 443:383-394, 2015.	pl_PL
dc.references	M. Dumnicki, D. Harrer, and J. Szpond. On absolute linear Harbourne constants. Finite Fields Appl., 51:371-387, 2018.	pl_PL
dc.references	M. Dumnicki, T. Szemberg, and H. Tutaj-Gasińska. Counterexamples to the I(3) I2 containment. J. Algebra, 393:24-29, 2013.	pl_PL
dc.references	L. Ein, R. Lazarsfeld, and K. E. Smith. Uniform bounds and symbolic powers on smooth varieties. Invent. Math., 144(2):241-{252, 2001.	pl_PL
dc.references	L. Farnik, F. Galuppi, L. Sodomaco, and W. Trok. On the unique unexpected quartic in P2. arXiv:1804.03590.	pl_PL
dc.references	Z. Furedi and I. Palasti. Arrangements of lines with a large number of triangles. Proc. Amer. Math. Soc., 92(4):561-566, 1984.	pl_PL
dc.references	A. V. Geramita, B. Harbourne, and J. Migliore. Star con gurations in Pn. J. Algebra, 376:279-299, 2013.	pl_PL
dc.references	B. Green and T. Tao. On sets de ning few ordinary lines. Discrete Comput. Geom., 50(2):409-468, 2013.	pl_PL
dc.references	E. Grifo, C. Huneke, and V. Mukundan. Expected resurgences and symbolic powers of ideals, arXiv:1903.12122.	pl_PL
dc.references	K. Hanumanthu and B. Harbourne. Real and complex supersolvable line arrangements in the projective plane, arXiv:1907.07712.	pl_PL
dc.references	B. Harbourne and C. Huneke. Are symbolic powers highly evolved? J. Ramanujan Math. Soc., 28A:247-266, 2013.	pl_PL
dc.references	B. Harbourne and A. Seceleanu. Containment counterexamples for ideals of various con gurations of points in PN. J. Pure Appl. Algebra, 219(4):1062-1072, 2015.	pl_PL
dc.references	O. Hesse. Uber die Elimination der Variabeln aus drei algebraischen Gleichungen vom zweiten Grade mit zwei Variabeln. J. Reine Angew. Math., 28:68-96, 1844.	pl_PL
dc.references	F. Hirzebruch. Arrangements of lines and algebraic surfaces. In Arithmetic and geometry, Vol. II, volume 36 of Progr. Math., pages 113{140. Birkhauser, Boston, Mass., 1983.	pl_PL
dc.references	M. Hochster and C. Huneke. Comparison of symbolic and ordinary powers of ideals. Invent. Math., 147(2):349-369, 2002.	pl_PL
dc.references	J. Jackson. Rational Amusement for Winter Evenings. Longman, Hurst, Rees, Orme and Brown, London, 1821.	pl_PL
dc.references	L. M. Kelly and W. O. J. Moser. On the number of ordinary lines determined by n points. Canadian J. Math., 10:210-219, 1958.	pl_PL
dc.references	C. W. H. Lam. The search for a nite projective plane of order 10 [ MR1103185 (92b:51013)]. In Organic mathematics (Burnaby, BC, 1995), volume 20 of CMS Conf. Proc., pages 335{ 355. Amer. Math. Soc., Providence, RI, 1997.	pl_PL
dc.references	M. Lampa-Baczyńska and J. Szpond. From Pappus Theorem to parameter spaces of some extremal line point con gurations and applications. Geom. Dedicata, 188:103-121, 2017.	pl_PL
dc.references	L. Ma and K. Schwede. Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers. Invent. Math., 214(2):913-955, 2018.	pl_PL
dc.references	E. Melchior. Uber Vielseite der projektiven Ebene. Deutsche Math., 5:461-475, 1941.	pl_PL
dc.references	T. Motzkin. The lines and planes connecting the points of a nite set. Trans. Amer. Math. Soc., 70:451-464, 1951.	pl_PL
dc.references	P. Pokora. Extremal properties of line arrangements in the complex projective plane, in this volume.	pl_PL
dc.references	I. Swanson. Linear equivalence of ideal topologies. Math. Z., 234(4):755-775, 2000.	pl_PL
dc.references	J. J. Sylvester. Problem 11851, Math. Questions from the Educational Times 59 (1893), 98-99.	pl_PL
dc.references	J. Szpond. On Hirzebruch type inequalities and applications. In Extended abstracts February 2016\|positivity and valuations, volume 9 of Trends Math. Res. Perspect. CRM Barc., pages 89-94. Birkh auser/Springer, Cham, 2018.	pl_PL
dc.references	J. Szpond. Fermat-type arrangements, arXiv:1909.04089.	pl_PL
dc.contributor.authorEmail	szpond@up.krakow.pl	pl_PL
dc.identifier.doi	10.18778/8142-814-9.15