On strengthening of the Kleiman-Chevalley projectivity criterion
HTML articles powered by AMS MathViewer
- by Michał Farnik PDF
- Proc. Amer. Math. Soc. 141 (2013), 4005-4013 Request permission
Abstract:
We discuss the possibilities of strengthening the classical Kleiman-Chevalley projectivity criterion by exploring the properties of the Picard number and the maximal quasiprojective open subsets of a variety. We also prove two theorems which give a bound on how much the criterion can be strengthened.References
- A. Białynicki-Birula, Finiteness of the number of maximal open subsets with good quotients, Transform. Groups 3 (1998), no. 4, 301–319. MR 1657520, DOI 10.1007/BF01234530
- MichałFarnik and Zbigniew Jelonek, A complete variety with infinitely many maximal quasi-projective open subsets, Demonstratio Math. 43 (2010), no. 2, 277–284. MR 2668476
- William Fulton, Introduction to toric varieties, Annals of Mathematics Studies, vol. 131, Princeton University Press, Princeton, NJ, 1993. The William H. Roever Lectures in Geometry. MR 1234037, DOI 10.1515/9781400882526
- H. Hironaka, On the theory of birational blowing up, Thesis, Harvard, 1960.
- Christopher D. Hacon and James McKernan, Flips and flops, Proceedings of the International Congress of Mathematicians. Volume II, Hindustan Book Agency, New Delhi, 2010, pp. 513–539. MR 2827807
- Zbigniew Jelonek, On the projectivity of threefolds, Proc. Amer. Math. Soc. 133 (2005), no. 9, 2539–2542. MR 2146196, DOI 10.1090/S0002-9939-05-07859-7
- Steven L. Kleiman, Toward a numerical theory of ampleness, Ann. of Math. (2) 84 (1966), 293–344. MR 206009, DOI 10.2307/1970447
- János Kollár, Rational curves on algebraic varieties, 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], vol. 32, Springer-Verlag, Berlin, 1996. MR 1440180, DOI 10.1007/978-3-662-03276-3
- G. Kempf, Finn Faye Knudsen, D. Mumford, and B. Saint-Donat, Toroidal embeddings. I, Lecture Notes in Mathematics, Vol. 339, Springer-Verlag, Berlin-New York, 1973. MR 0335518
- Igor R. Shafarevich, Basic algebraic geometry. 2, 2nd ed., Springer-Verlag, Berlin, 1994. Schemes and complex manifolds; Translated from the 1988 Russian edition by Miles Reid. MR 1328834
- Jarosław Włodarczyk, Embeddings in toric varieties and prevarieties, J. Algebraic Geom. 2 (1993), no. 4, 705–726. MR 1227474
- Jarosław Włodarczyk, Maximal quasiprojective subsets and the Kleiman-Chevalley quasiprojectivity criterion, J. Math. Sci. Univ. Tokyo 6 (1999), no. 1, 41–47. MR 1683254
Additional Information
- Michał Farnik
- Affiliation: Instytut Matematyczny, Polska Akademia Nauk, św. Tomasza 30, 31-027 Kraków, Poland
- Address at time of publication: Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956 Warszawa, Poland
- Email: michal.farnik@gmail.com
- Received by editor(s): June 15, 2011
- Received by editor(s) in revised form: January 7, 2012
- Published electronically: July 10, 2013
- Additional Notes: The author was partially supported by Polish MNiSW grant N N201 611740, 2011–2012
- Communicated by: Lev Borisov
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 4005-4013
- MSC (2010): Primary 51N35; Secondary 14A10, 14M25
- DOI: https://doi.org/10.1090/S0002-9939-2013-11695-3
- MathSciNet review: 3091791