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Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone
An arithmetic ball quotient surface whose Albanese variety is not of CM type
1. | Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, United States |
References:
[1] |
T. Chinburg and M. Stover, Arizona winter school course lecture notes, 2012. Available from: http://swc.math.arizona.edu/aws/2012/index.html. |
[2] |
D. Cox, Primes of the Form $x^2+ny^2$, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1989. |
[3] |
J. Cremona, Algorithms for Modular Elliptic Curves, Second edition, Cambridge University Press, Cambridge, 1997. |
[4] |
F. Diamond and J. Shurman, A First Course in Modular Forms, Graduate Texts in Mathematics, 228, Springer-Verlag, New York, 2005. |
[5] |
N. Elkies, The Klein Quartic in Number Theory, in The Eightfold Way, Math. Sci. Res. Inst. Publ., 35, Cambridge Univ. Press, Cambridge, 1999, 51-101. |
[6] |
R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York, 1977. |
[7] |
F. Hirzebruch, Arrangements of lines and algebraic surfaces, Arithmetic and Geometry, Vol. II, Progr. Math., 36, Birkhäuser, Boston, Mass., 1983, 113-140. |
[8] |
M. Inoue, Some new surfaces of general type, Tokyo J. Math., 17 (1994), 295-319.
doi: 10.3836/tjm/1270127954. |
[9] |
M.-N. Ishida, The irregularities of Hirzebruch's examples of surfaces of general type with $c_1^2=3c_2$, Math. Ann., 262 (1983), 407-420.
doi: 10.1007/BF01456018. |
[10] |
S. Lang, Abelain Varieties, Interscience Tracts in Pure and Applied Mathematics. No. 7, Interscience Publishers, Inc., New York, 1959. |
[11] |
R. Livné, On Certain Covers of the Universal Elliptic Curve, Ph.D. Thesis, Harvard University, 1981. |
[12] |
Y. Miyoaka, The maximal number of quotients singularities on surfaces with given numerical invariants, Math. Ann., 268 (1984), 159-171.
doi: 10.1007/BF01456083. |
[13] |
K. Murty and D. Ramakrishnan, The Albanese of unitary Shimura varieties, in The Zeta Function of Picard Modular Surfaces (eds. R. Langlands and D. Ramakrishnan), Univ. Montréal, Montréal, 1992, 445-464. |
[14] |
J. D. Rogawski, Analytic expression for the number of points mod $p$, in The Zeta Function of Picard Modular Surfaces (eds. R. Langlands and D. Ramakrishnan), Univ. Montréal, Montréal, 1992, 65-109. |
[15] |
J. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 106, Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4757-1920-8. |
[16] |
J. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 151, Springer-Verlag, New York, 1994.
doi: 10.1007/978-1-4612-0851-8. |
[17] |
R. O. Wells, Differential Analysis on Complex Manifolds, Prentice-Hall Series in Modern Analysis, Prentice Hall, Inc., Englewood Cliffs, NJ, 1973. |
[18] |
T. Yamazaki and M. Yoshida, On Hirzebruch's examples of surfaces with $c_1^2=3c_2$, Math. Ann., 266 (1984), 421-431.
doi: 10.1007/BF01458537. |
[19] |
S.-T. Yau, Calabi's conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci. USA, 74 (1977), 1798-1799.
doi: 10.1073/pnas.74.5.1798. |
show all references
References:
[1] |
T. Chinburg and M. Stover, Arizona winter school course lecture notes, 2012. Available from: http://swc.math.arizona.edu/aws/2012/index.html. |
[2] |
D. Cox, Primes of the Form $x^2+ny^2$, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1989. |
[3] |
J. Cremona, Algorithms for Modular Elliptic Curves, Second edition, Cambridge University Press, Cambridge, 1997. |
[4] |
F. Diamond and J. Shurman, A First Course in Modular Forms, Graduate Texts in Mathematics, 228, Springer-Verlag, New York, 2005. |
[5] |
N. Elkies, The Klein Quartic in Number Theory, in The Eightfold Way, Math. Sci. Res. Inst. Publ., 35, Cambridge Univ. Press, Cambridge, 1999, 51-101. |
[6] |
R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York, 1977. |
[7] |
F. Hirzebruch, Arrangements of lines and algebraic surfaces, Arithmetic and Geometry, Vol. II, Progr. Math., 36, Birkhäuser, Boston, Mass., 1983, 113-140. |
[8] |
M. Inoue, Some new surfaces of general type, Tokyo J. Math., 17 (1994), 295-319.
doi: 10.3836/tjm/1270127954. |
[9] |
M.-N. Ishida, The irregularities of Hirzebruch's examples of surfaces of general type with $c_1^2=3c_2$, Math. Ann., 262 (1983), 407-420.
doi: 10.1007/BF01456018. |
[10] |
S. Lang, Abelain Varieties, Interscience Tracts in Pure and Applied Mathematics. No. 7, Interscience Publishers, Inc., New York, 1959. |
[11] |
R. Livné, On Certain Covers of the Universal Elliptic Curve, Ph.D. Thesis, Harvard University, 1981. |
[12] |
Y. Miyoaka, The maximal number of quotients singularities on surfaces with given numerical invariants, Math. Ann., 268 (1984), 159-171.
doi: 10.1007/BF01456083. |
[13] |
K. Murty and D. Ramakrishnan, The Albanese of unitary Shimura varieties, in The Zeta Function of Picard Modular Surfaces (eds. R. Langlands and D. Ramakrishnan), Univ. Montréal, Montréal, 1992, 445-464. |
[14] |
J. D. Rogawski, Analytic expression for the number of points mod $p$, in The Zeta Function of Picard Modular Surfaces (eds. R. Langlands and D. Ramakrishnan), Univ. Montréal, Montréal, 1992, 65-109. |
[15] |
J. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 106, Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4757-1920-8. |
[16] |
J. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 151, Springer-Verlag, New York, 1994.
doi: 10.1007/978-1-4612-0851-8. |
[17] |
R. O. Wells, Differential Analysis on Complex Manifolds, Prentice-Hall Series in Modern Analysis, Prentice Hall, Inc., Englewood Cliffs, NJ, 1973. |
[18] |
T. Yamazaki and M. Yoshida, On Hirzebruch's examples of surfaces with $c_1^2=3c_2$, Math. Ann., 266 (1984), 421-431.
doi: 10.1007/BF01458537. |
[19] |
S.-T. Yau, Calabi's conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci. USA, 74 (1977), 1798-1799.
doi: 10.1073/pnas.74.5.1798. |
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