Kodaira dimension of symmetric powers
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- by Donu Arapura and Sviatoslav Archava PDF
- Proc. Amer. Math. Soc. 131 (2003), 1369-1372 Request permission
Abstract:
We compute the plurigenera and the Kodaira dimension of the $d$th symmetric power $S^dX$ of a smooth projective variety $X$. As an application we obtain genus estimates for the curves lying on $X$.References
- Daniel Huybrechts and Manfred Lehn, The geometry of moduli spaces of sheaves, Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschweig, 1997. MR 1450870, DOI 10.1007/978-3-663-11624-0
- 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
- Shigefumi Mori, Classification of higher-dimensional varieties, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 269–331. MR 927961
- D. Mumford, Rational equivalence of $0$-cycles on surfaces, J. Math. Kyoto Univ. 9 (1968), 195–204. MR 249428, DOI 10.1215/kjm/1250523940
- Miles Reid, Canonical $3$-folds, Journées de Géometrie Algébrique d’Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, Sijthoff & Noordhoff, Alphen aan den Rijn—Germantown, Md., 1980, pp. 273–310. MR 605348
- A. A. Roĭtman, ${G}$-equivalence of zero-dimensional cycles, Mat. Sb. (N.S.) 86 (128) (1971), 557–570 (Russian). MR 0289512
- A. A. Roĭtman, Rational equivalence of zero-dimensional cycles, Mat. Sb. (N.S.) 89(131) (1972), 569–585, 671 (Russian). MR 0327767
- Keiichi Watanabe, Certain invariant subrings are Gorenstein. I, II, Osaka Math. J. 11 (1974), 1–8; ibid. 11 (1974), 379–388. MR 354646
Additional Information
- Donu Arapura
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 26770
- Email: arapura@math.purdue.edu
- Sviatoslav Archava
- Affiliation: MPI für Mathematik, Vivatgasse 7, D-53111, Bonn, Germany
- Received by editor(s): September 1, 2000
- Received by editor(s) in revised form: January 9, 2002
- Published electronically: October 1, 2002
- Additional Notes: The authors were partially supported by the NSF
- Communicated by: Michael Stillman
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1369-1372
- MSC (2000): Primary 14J40, 14E08
- DOI: https://doi.org/10.1090/S0002-9939-02-06797-7
- MathSciNet review: 1949866