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On bounded cocycles of isometries over minimal dynamics
The Cayley-Oguiso automorphism of positive entropy on a K3 surface
1. | Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, 2333 Leiden, Netherlands, Netherlands |
2. | Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy, Italy |
References:
[1] |
M. F. Atiyah and I. G. Macdonald, "Introduction to Commutative Algebra," Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. |
[2] |
W. P. Barth, K. Hulek, C. A. M. Peters and A. Van de Ven, "Compact Complex Surfaces," Second edition, 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], 4, Springer-Verlag, Berlin, 2004. |
[3] |
L. Bădescu, "Algebraic Surfaces," Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author, Universitext, Springer-Verlag, New York, 2001. |
[4] |
A. Beauville, Determinantal Hypersurfaces, Michigan Math. J., 48 (2000), 39-64.
doi: 10.1307/mmj/1030132707. |
[5] |
S. Cantat, A. Chambert-Loir and V. Guedj, "Quelques Aspects des Systèmes Dynamiques Polynomiaux," Panoramas et Synthèses, 30, Société Mathématique de France, Paris, 2010. |
[6] |
A. Cayley, A memoir on quartic surfaces,, Proc. London Math. Soc., 3 (): 1869.
|
[7] |
I. Dolgachev, "Classical Algebraic Geometry: A Modern View," Cambridge University Press, Cambridge, 2012.
doi: 10.1017/CBO9781139084437. |
[8] |
W. Fulton, "Intersection Theory," Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 2, Springer-Verlag, Berlin, 1984. |
[9] |
D. Festi, A. Garbagnati, B. van Geemen and R. van Luijk, Computations for Sections 4 and 5., Available from: \url{http://www.math.leidenuniv.nl/~rvl/CayleyOguiso}., ().
|
[10] |
A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math., 24 (1965), 231 pp. |
[11] |
R. Hartshorne, "Algebraic Geometry," Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. |
[12] |
Q. Liu, "Algebraic Geometry and Arithmetic Curves," Translated from the French by Reinie Erné, Oxford Graduate Texts in Mathematics, 6, Oxford Science Publications, Oxford University Press, Oxford, 2002. |
[13] |
R. van Luijk, An elliptic K3 surface associated to Heron triangles, J. Number Theory, 123 (2007), 92-119.
doi: 10.1016/j.jnt.2006.06.006. |
[14] |
R. van Luijk, K3 surfaces with Picard number one and infinitely many rational points, Algebra and Number Theory, 1 (2007), 1-15.
doi: 10.2140/ant.2007.1.1. |
[15] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[16] |
J. S. Milne, "Étale Cohomology," Princeton Mathematical Series, 33, Princeton University Press, Princeton, N.J., 1980. |
[17] |
K. Oguiso, Free automorphisms of positive entropy on smooth Kähler surfaces,, to appear in Adv. Stud. Pure Math., ().
|
[18] |
T. G. Room, Self-transformations of determinantal quartic surfaces. I, Proc. London Math. Soc. (2), 51 (1950), 348-361.
doi: 10.1112/plms/s2-51.5.348. |
[19] |
T. G. Room, Self-transformations of determinantal quartic surfaces. II, Proc. London Math. Soc. (2), 51 (1950), 362-382.
doi: 10.1112/plms/s2-51.5.362. |
[20] |
T. G. Room, Self-transformations of determinantal quartic surfaces. III, Proc. London Math. Soc. (2), 51 (1950), 383-387.
doi: 10.1112/plms/s2-51.5.383. |
[21] |
T. G. Room, Self-transformations of determinantal quartic surfaces. IV, Proc. London Math. Soc. (2), 51 (1950), 388-400.
doi: 10.1112/plms/s2-51.5.388. |
[22] |
B. Saint-Donat, Projective models of K-3 surfaces, Amer. J. Math., 96 (1974), 602-639.
doi: 10.2307/2373709. |
[23] |
F. Schur, Über die durch collineare Grundgebilde erzeugten Curven und Flächen, Math. Ann., 18 (1881), 1-32.
doi: 10.1007/BF01443653. |
[24] |
V. Snyder and F. R. Sharpe, Certain quartic surfaces belonging to infinite discontinuous Cremonian groups, Trans. Amer. Math. Soc., 16 (1915), 62-70.
doi: 10.1090/S0002-9947-1915-1501000-2. |
[25] |
J. T. Tate, Algebraic cycles and poles of zeta functions, in "Arithmetical Algebraic Geometry" (Proc. Conf. Purdue Univ., 1963), Harper & Row, New York, (1965), 93-110. |
show all references
References:
[1] |
M. F. Atiyah and I. G. Macdonald, "Introduction to Commutative Algebra," Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. |
[2] |
W. P. Barth, K. Hulek, C. A. M. Peters and A. Van de Ven, "Compact Complex Surfaces," Second edition, 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], 4, Springer-Verlag, Berlin, 2004. |
[3] |
L. Bădescu, "Algebraic Surfaces," Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author, Universitext, Springer-Verlag, New York, 2001. |
[4] |
A. Beauville, Determinantal Hypersurfaces, Michigan Math. J., 48 (2000), 39-64.
doi: 10.1307/mmj/1030132707. |
[5] |
S. Cantat, A. Chambert-Loir and V. Guedj, "Quelques Aspects des Systèmes Dynamiques Polynomiaux," Panoramas et Synthèses, 30, Société Mathématique de France, Paris, 2010. |
[6] |
A. Cayley, A memoir on quartic surfaces,, Proc. London Math. Soc., 3 (): 1869.
|
[7] |
I. Dolgachev, "Classical Algebraic Geometry: A Modern View," Cambridge University Press, Cambridge, 2012.
doi: 10.1017/CBO9781139084437. |
[8] |
W. Fulton, "Intersection Theory," Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 2, Springer-Verlag, Berlin, 1984. |
[9] |
D. Festi, A. Garbagnati, B. van Geemen and R. van Luijk, Computations for Sections 4 and 5., Available from: \url{http://www.math.leidenuniv.nl/~rvl/CayleyOguiso}., ().
|
[10] |
A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math., 24 (1965), 231 pp. |
[11] |
R. Hartshorne, "Algebraic Geometry," Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. |
[12] |
Q. Liu, "Algebraic Geometry and Arithmetic Curves," Translated from the French by Reinie Erné, Oxford Graduate Texts in Mathematics, 6, Oxford Science Publications, Oxford University Press, Oxford, 2002. |
[13] |
R. van Luijk, An elliptic K3 surface associated to Heron triangles, J. Number Theory, 123 (2007), 92-119.
doi: 10.1016/j.jnt.2006.06.006. |
[14] |
R. van Luijk, K3 surfaces with Picard number one and infinitely many rational points, Algebra and Number Theory, 1 (2007), 1-15.
doi: 10.2140/ant.2007.1.1. |
[15] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[16] |
J. S. Milne, "Étale Cohomology," Princeton Mathematical Series, 33, Princeton University Press, Princeton, N.J., 1980. |
[17] |
K. Oguiso, Free automorphisms of positive entropy on smooth Kähler surfaces,, to appear in Adv. Stud. Pure Math., ().
|
[18] |
T. G. Room, Self-transformations of determinantal quartic surfaces. I, Proc. London Math. Soc. (2), 51 (1950), 348-361.
doi: 10.1112/plms/s2-51.5.348. |
[19] |
T. G. Room, Self-transformations of determinantal quartic surfaces. II, Proc. London Math. Soc. (2), 51 (1950), 362-382.
doi: 10.1112/plms/s2-51.5.362. |
[20] |
T. G. Room, Self-transformations of determinantal quartic surfaces. III, Proc. London Math. Soc. (2), 51 (1950), 383-387.
doi: 10.1112/plms/s2-51.5.383. |
[21] |
T. G. Room, Self-transformations of determinantal quartic surfaces. IV, Proc. London Math. Soc. (2), 51 (1950), 388-400.
doi: 10.1112/plms/s2-51.5.388. |
[22] |
B. Saint-Donat, Projective models of K-3 surfaces, Amer. J. Math., 96 (1974), 602-639.
doi: 10.2307/2373709. |
[23] |
F. Schur, Über die durch collineare Grundgebilde erzeugten Curven und Flächen, Math. Ann., 18 (1881), 1-32.
doi: 10.1007/BF01443653. |
[24] |
V. Snyder and F. R. Sharpe, Certain quartic surfaces belonging to infinite discontinuous Cremonian groups, Trans. Amer. Math. Soc., 16 (1915), 62-70.
doi: 10.1090/S0002-9947-1915-1501000-2. |
[25] |
J. T. Tate, Algebraic cycles and poles of zeta functions, in "Arithmetical Algebraic Geometry" (Proc. Conf. Purdue Univ., 1963), Harper & Row, New York, (1965), 93-110. |
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