On planar Cremona maps of prime order

Nagoya Mathematical Journal

Volumn 174, Issue , 2004, Pages 1-28

  De Fernex, Tommaso ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344670834     PISSN: 00277630     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0027763000008795     Document Type: Article

References (29)

1. M. Alberich-Caraminana, Geometry of the Plane Cremona Maps, Lectures Notes in Math., 1769 (2002), Springer-Verlag, Berlin.
2. L. Autonne, Reserches sur les groupes d'ordre fini contenus dans le groupe Cremona, J. Math. Pures et Appl. (1885).
3. W. Barth, C. Peters and A. Van de Ven, Compact Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, 4, Springer-Verlag, Berlin, 1984.
4. 2, Asian J. Math., 4(1) (2000), 11-18.
5. A. Beauville, On Cremona transformations of prime order, Preprint available at ArXiv:math.AG/0402037.
6. E. Bertini, Ricerche sulle trasformazioni univoche involutorie nel piano, Annali di Mat., 8 (1877), 244-286.
7. n√F(x,y)}, Ann. Mat. Pura Appl., Serie III, 2 (1899), 277-296.
8. A. Calabri, On rational and ruled double planes, Ann. Mat. Pura Appl., 181(4) (2002), 365-387.
9. _, On rational cyclic triple planes, Preprint (2001).
10. G. Castelnuovo and F. Enriques, Sulle condizioni di razionalità dei piani doppi, Rend. del Circ. Mat. di Palermo, 14 (1900), 290-302.
11. T. de Fernex and L. Ein, Resolution of indeterminacy of pairs, in Algebraic Geometry, a Volume in Memory of Paolo Francia, eds. M. Beltrametti et al. (2002), de Gruiter.
12. W. Engel, Invariante Divisorensharen dei endlichen Gruppen von Cremonatrans formationen, J. Reine Angew. Math., 196 (1956), 59-66.
13. T. Fujita, Classification theories of polarized varieties, London Mathematical Society Lecture Note Series, 155 (1990), Cambridge Univ. Press, Cambridge.
14. M. H. Gizatullin, Rational G-surfaces, Izv. Akad. Nauk SSSR Ser. Mat., 44(1) (1980), 110-144, 239.
15. L. Godeaux, Une représentation des transformations birationnelles du plan et de l'espace, Acad. Roy. Belgique. Cl. Sci. Mém. Coll. in 8°. (2), 24(2) (1949), 31.
16. R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York, 1977, pp. xvi+496.
17. T. Hosoh, Automorphism groups of quartic del Pezzo surfaces, J. Algebra, 185(2) (1996), 374-389.
18. _, Automorphism groups of cubic surfaces, J. Algebra, 192(2) (1997), 651-677.
19. S. Kantor, Theorie der endlichen Gruppen von eindeutigen Transformationen in der Ebene, Mayer & Müller, Berlin, 1895.
20. M. Koitabashi, Automorphism groups of generic rational surfaces, J. Algebra, 116(1) (1988), 130-142.
21. J. Kollár and S. Mori, Birational geometry of algebraic varieties, With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original, Cambridge University Press, Cambridge, 1998, pp. viii+254.
22. Yu. I. Manin, Rational surfaces over perfect fields. II., Math. USSR Sb., 1 (1967), 141-168.
23. _, Cubic forms: algebra, geometry, arithmetic, Translated from Russian by M. Hazewinkel, North-Holland Mathematical Library, Vol. 4, North-Holland Publishing Co., Amsterdam, 1974, pp. vii+292.
24. R. Miranda and U. Persson, On extremal rational elliptic surfaces, Math. Z., 193(4) (1986), 537-558.
25. S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. (2), 116(1) (1982), 133-176.
26. B. Segre, The non-singular cubic surface (1942), Oxford University Press, Oxford.
27. A. Wiman, Zur theorie der endlichen gruppen von birazionalen transformationen in der ebene, Math. Ann., 4 (1897).
28. D.-Q. Zhang, Automorphisms of finite order on rational surfaces, J. Algebra, 238(2) (2001), 560-589.
29. _, Automorphisms of finite order on Gorenstein del Pezzo surfaces, Trans. Amer. Math. Soc., 354(12) (2002), 4831-4845.