An invitation to the positivity and geometry of algebraic cycles

Szpond, Justyna

dc.contributor.author	Szpond, Justyna
dc.contributor.editor	Krasiński, Tadeusz
dc.contributor.editor	Spodzieja, Stanisław
dc.date.accessioned	2022-12-22T15:47:47Z
dc.date.available	2022-12-22T15:47:47Z
dc.date.issued	2022
dc.identifier.citation	Szpond J., An invitation to the positivity and geometry of algebraic cycles, [in:] Analitic and Algebraic Geometry 4, T. Krasiński, S. Spodzieja (ed.), WUŁ, Łódź 2022, https://doi.org/10.18778/8331-092-3.13	pl_PL
dc.identifier.isbn	978-83-8331-092-3
dc.identifier.uri	http://hdl.handle.net/11089/44820
dc.description.abstract	The purpose of this work is an introduction and overview of geometric and numeric properties of algebraic cycles in smooth projective varieties. We recall or propose several problems, which we consider worth to study. We are mainly interested in, but do not restrict our story to, codimension 2 cycles in projective spaces. These are points in P^2, curves in P^3, surfaces in P^4 and so on.	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.subject	algebraic cycles	pl_PL
dc.subject	Hartshorne conjecture	pl_PL
dc.subject	space curves	pl_PL
dc.subject	ACM subvarieties	pl_PL
dc.title	An invitation to the positivity and geometry of algebraic cycles	pl_PL
dc.type	Book chapter	pl_PL
dc.page.number	163-173	pl_PL
dc.contributor.authorAffiliation	Uniwersytet Pedagogiczny w Krakowie, Instytut Matematyki	pl_PL
dc.identifier.eisbn	978-83-8331-093-0
dc.references	T. Aladpoosh, Postulation of generic lines and one double line in Pn in view of generic lines and one multiple linear space. Selecta Math. (N.S.) 25 (2019), no. 1, Paper No. 9, 45 pp.	pl_PL
dc.references	A. Atanasov, E. Larson, D. Yang, Interpolation for normal bundles of general curves. Mem. Amer. Math. Soc. 257 (2019), no. 1234, v+105 pp.	pl_PL
dc.references	T. Bauer, S. Di Rocco, D. Schmitz, T. Szemberg, J. Szpond, On the postulation of lines and a fat line. J. Symbolic Comput. 91 (2019), 3–16.	pl_PL
dc.references	A. Bertram, L. Ein, R. Lazarsfeld, Vanishing theorems, a theorem of Severi, and the equations defining projective varieties. J. Amer. Math. Soc. 4 (1991), no. 3, 587–602.	pl_PL
dc.references	C. Bocci, L. Chiantini, The effect of points fattening on postulation. J. Pure Appl. Algebra 215 (2011), no. 1, 89–98.	pl_PL
dc.references	S. Boucksom, J.-P. Demailly, M. P˘aun, T. Peternell, The pseudo-effective cone of a compact K¨ahler manifold and varieties of negative Kodaira dimension. J. Algebraic Geom. 22 (2013), no. 2, 201–248.	pl_PL
dc.references	M. Dumnicki, B. Harbourne, J. Ro´e, T. Szemberg, H. Tutaj-Gasi´nska, Unexpected surfaces singular on lines in P3. Eur. J. Math. 7 (2021), no. 2, 570–590.	pl_PL
dc.references	M. Z. Fashami, H. Haghighi, T. Szemberg, Fattening of ACM arrangements of codimension 2 subspaces in PN. J. Algebra Appl. 19 (2020), no. 3, 2050056, 10 pp.	pl_PL
dc.references	F. Gaeta, Sulle famiglie di curve sghembe algebriche. Boll. Un. Mat. Ital. (3) 5, (1950), 149–156.	pl_PL
dc.references	A. V. Geramita, B. Harbourne, J. Migliore, Star configurations in Pn. J. Algebra 376 (2013), 279–299.	pl_PL
dc.references	P. Griffiths, J. Harris, On the Noether-Lefschetz theorem and some remarks on codimensiontwo cycles. Math. Ann. 271 (1985), no. 1, 31–51.	pl_PL
dc.references	L. Gruson, R. Lazarsfeld, C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves. Invent. Math. 72 (1983), no. 3, 491–506.	pl_PL
dc.references	L. Gruson and C. Peskine, Genre des courbes de l’espace projectif. In Algebraic geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977), volume 687 of Lecture Notes in Math., pages 31–59. Springer, Berlin, 1978.	pl_PL
dc.references	R. Hartshorne, Varieties of small codimension in projective space. Bull. Amer. Math. Soc. 80 (1974), 1017–1032.	pl_PL
dc.references	R. Hartshorne, A. Hirschowitz, Droites en position g´en´erale dans l’espace projectif. In Algebraic geometry (La R´abida, 1981), volume 961 of Lecture Notes in Math., pages 169–188. Springer, Berlin, 1982.	pl_PL
dc.references	A. Holme, M. Schneider, A computer aided approach to codimension 2 subvarieties of Pn, n ≧ 6. J. Reine Angew. Math. 357 (1985), 205–220.	pl_PL
dc.references	G. Horrocks, D. Mumford, A rank 2 vector bundle on P4 with 15, 000 symmetries. Topology 12 (1973), 63–81.	pl_PL
dc.references	M. Janssen, On the fattening of lines in P3. J. Pure Appl. Algebra 219 (2015), no. 4, 1055–1061.	pl_PL
dc.references	R. Lazarsfeld, Positivity in algebraic geometry., volume 48, 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series.	pl_PL
dc.references	B. Lehmann, Volume-type functions for numerical cycle classes. Duke Math. J. 165 (2016), no. 16, 3147–3187.	pl_PL
dc.references	B. Lehmann, J. Xiao, Correspondences between convex geometry and complex geometry. ´Epijournal Geom. Alg´ebrique 1 (2017), Art. 6, 29 pp.	pl_PL
dc.references	J. McCullough, I. Peeva, Counterexamples to the Eisenbud-Goto regularity conjecture. J. Amer. Math. Soc. 31 (2018), no. 2, 473–496.	pl_PL
dc.references	J. C. Migliore, U. Nagel, Glicci ideals. Compos. Math. 149 (2013), no. 9, 1583–1591.	pl_PL
dc.references	J. C. Migliore, Introduction to liaison theory and deficiency modules, volume 165 of Progress in Mathematics. Birkh¨auser Boston, Inc., Boston, MA, 1998.	pl_PL
dc.references	D. Perrin, Courbes passant par k points g´en´eraux de P3. C. R. Acad. Sci. Paris S´er. I Math. 299 (1984), no. 10, 451–453.	pl_PL
dc.references	Z. Ran, On projective varieties of codimension 2. Invent. Math. 73 (1983), no. 2, 333–336.	pl_PL
dc.references	J. Szpond, Fermat-type arrangements. In Combinatorial structures in algebra and geometry, volume 331 of Springer Proc. Math. Stat., pages 161–182. Springer, Cham, 2020.	pl_PL
dc.references	I. Vogt, Interpolation for Brill-Noether space curves. Manuscripta Math. 156 (2018), no. 1–2, 137–147.	pl_PL
dc.references	D. Witt Nystr¨om, Duality between the pseudoeffective and the movable cone on a projective manifold. J. Amer. Math. Soc. 32 (2019), no. 3, 675–689. With an appendix by S´ebastien Boucksom.	pl_PL
dc.references	J. Xiao, Characterizing volume via cone duality. Math. Ann. 369 (2017), no. 3–4, 1527–1555.	pl_PL
dc.contributor.authorEmail	szpond@up.krakow.pl	pl_PL
dc.identifier.doi	10.18778/8331-092-3.13