Parametrization of rational maps on a variety of general type, and the finiteness theorem
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- by Lucio Guerra and Gian Pietro Pirola PDF
- Proc. Amer. Math. Soc. 142 (2014), 93-100 Request permission
Abstract:
In a previous paper we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing the natural parametrization of maps by means of the space of linear projections in a suitable projective space, and this leads to some new insight into the geometry of the finiteness theorem.References
- Jungkai A. Chen and Meng Chen, Explicit birational geometry of 3-folds of general type, II, J. Differential Geom. 86 (2010), no. 2, 237–271. MR 2772551
- William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620, DOI 10.1007/978-3-662-02421-8
- Lucio Guerra and Gian Pietro Pirola, On the finiteness theorem for rational maps on a variety of general type, Collect. Math. 60 (2009), no. 3, 261–276. MR 2560970, DOI 10.1007/BF03191371
- Christopher D. Hacon and James McKernan, Boundedness of pluricanonical maps of varieties of general type, Invent. Math. 166 (2006), no. 1, 1–25. MR 2242631, DOI 10.1007/s00222-006-0504-1
- Shoshichi Kobayashi and Takushiro Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math. 31 (1975), no. 1, 7–16. MR 402127, DOI 10.1007/BF01389863
- Robert Lazarsfeld, Positivity in algebraic geometry. I, 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. 48, Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. MR 2095471, DOI 10.1007/978-3-642-18808-4
- Kazuhisa Maehara, A finiteness property of varieties of general type, Math. Ann. 262 (1983), no. 1, 101–123. MR 690010, DOI 10.1007/BF01474173
- Shigeharu Takayama, Pluricanonical systems on algebraic varieties of general type, Invent. Math. 165 (2006), no. 3, 551–587. MR 2242627, DOI 10.1007/s00222-006-0503-2
- Shigeharu Takayama, On the invariance and the lower semi-continuity of plurigenera of algebraic varieties, J. Algebraic Geom. 16 (2007), no. 1, 1–18. MR 2257317, DOI 10.1090/S1056-3911-06-00455-3
Additional Information
- Lucio Guerra
- Affiliation: Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123 Perugia, Italia
- Email: lucio.guerra@unipg.it
- Gian Pietro Pirola
- Affiliation: Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia, Italia
- MR Author ID: 139965
- Email: gianpietro.pirola@unipv.it
- Received by editor(s): October 17, 2011
- Received by editor(s) in revised form: March 2, 2012
- Published electronically: September 27, 2013
- Communicated by: Lev Borisov
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 93-100
- MSC (2010): Primary 14E05, 14N05
- DOI: https://doi.org/10.1090/S0002-9939-2013-11750-8
- MathSciNet review: 3119184