On dominant rational maps from products of curves to surfaces of general type

• Autores: Francesco Bastianelli, Gian Pietro Pirola
• Localización: Bulletin of the London Mathematical Society, ISSN 0024-6093, Vol. 45, Nº 6, 2013, págs. 1310-1322
• Idioma: inglés
• DOI: 10.1112/blms/bdt057
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • E. Arbarello, M. Cornalba and P. A. Griffiths, Geometry of algebraic curves, Grundlehren der Mathematischen Wissenschaften II [Fundamental...
  • W. Barth, K. Hulek, C. Peters and A. Van de Ven, Compact complex surfaces, 2nd edn, Ergebnisse der Mathematik und ihrer Grenzgebiete 4 (Springer,...
  • I. Bauer and F. Catanese, ‘Some new surfaces with $p_g=q=0$’, The Fano Conference (Univ. Torino, Turin, 2004) 123–142.
  • I. Bauer, F. Catanese and F. Grunewald, ‘The classification of surfaces with $p_g=q=0$ isogenous to a product of curves’, Pure Appl....
  • I. Bauer and R. Pignatelli, ‘The classification of minimal product-quotient surfaces with $p_g=0$’, Math. Comp. 81 (2012) 2389–2418.
  • A. Beauville, Surfaces algébriques complexes, Astérisque 54 (Société Mathématique de France, Paris, 1978).
  • A. Beauville, Complex algebraic surfaces, 2nd edn, London Mathematical Society Student Texts 34 (Cambridge University Press, Cambridge, 1996).
  • L. Caporaso, J. Harris and B. Mazur, ‘Uniformity of rational points’, J. Amer. Math. Soc. 10 (1997) 1–35.
  • F. Catanese, ‘On the moduli spaces of surfaces of general type’, J. Differential Geom. 19 (1984) 483–515.
  • F. Catanese, ‘Fibred surfaces, varieties isogenous to a product and related moduli spaces’, Amer. J. Math. 122 (2000) 1–44.
  • C. Ciliberto and G. van der Geer, ‘On the Jacobian of a hyperplane section of a surface’, Classification of irregular varieties (Trento, 1990),...
  • E. Colombo and G. P. Pirola, ‘Some density results for curves with nonsimple Jacobians’, Math. Ann. 288 (1990) 161–178.
  • S. Díaz, ‘A bound on the dimensions of complete subvarieties of $M_g$’, Duke Math. J. 51 (1984) 405–408.
  • C. F. Faber, ‘Some results on the codimension-two Chow group of the moduli space of stable curves’, Algebraic curves and projective geometry...
  • P. A. Griffiths and J. Harris, Principles of algebraic geometry, Pure and Applied Mathematics (Wiley Interscience, New York, 1978).
  • L. Guerra, ‘Complexity of Chow varieties and number of morphisms on surfaces of general type’, Manuscripta Math. 98 (1999) 1–8.
  • L. Guerra and G. P. Pirola, ‘On rational maps from a general surface in $\mathbb{P}^3$ to surfaces of general type’, Adv. Geom. 8 (2008) 289–307.
  • L. Guerra and G. P. Pirola, ‘On the finiteness theorem for rational maps on a variety of general type’, Collect. Math. 60 (2009) 261–276.
  • L. Guerra and G. P. Pirola, ‘Parametrization of rational maps on a variety of general type, and the finiteness theorem’, Proc. Amer. Math....
  • C. D. Hacon and J. McKernan, ‘Boundedness of pluricanonical maps of varieties of general type’, Invent. Math. 166 (2006) 1–25.
  • J. Harris and I. Morrison, Moduli of curves, Graduate Texts in Mathematics 187 (Springer, New York, 1998).
  • G. Heier, ‘Effective finiteness theorems for maps between canonically polarized compact complex manifolds’, Math. Nachr. 278 (2005) 133–140.
  • E. Kani, ‘Bounds on the number of nonrational subfields of a function field’, Invent. Math. 85 (1986) 185–198.
  • J. Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas....
  • I. Krichever, ‘Real normalized differentials and compact cycles in the moduli space of curves’, Preprint, 2012, arXiv:1204.2192v1.
  • K. Maehara, ‘A finiteness property of varieties of general type’, Math. Ann. 262 (1983) 101–123.
  • S. Mori, ‘Projective manifolds with ample tangent bundles’, Ann. of Math. 110 (1979) 593–606.
  • D. Mumford and J. Fogarty, Geometric invariant theory, 2nd edn, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and...
  • M. A. Naimark and A. I. Stern, Theory of group representations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical...
  • J. C. Naranjo and G. P. Pirola, ‘Bounds of the number of rational maps between varieties of general type’, Amer. J. Math. 129 (2007) 1689–1709.
  • M. Penegini, ‘The classification of isotrivially fibred surfaces with $p_g=q=2$’, Collect. Math. 62 (2011) 239–274.
  • G. P. Pirola, ‘Curves on generic Kummer varieties’, Duke Math. J. 59 (1989) 701–708.
  • F. Polizzi, ‘Standard isotrivial fibrations with $p_g=q=1$’, J. Algebra 321 (2009) 1600–1631.
  • F. Serrano, ‘Isotrivial fibred surfaces’, Ann. Mat. Pura Appl. CLXXI (1996) 63–81.
  • F. Severi, ‘Le corrispondenze fra i punti di una curva variabile in un sistema lineare sopra una superficie algebrica’, Math. Ann. 74 (1913)...
  • S. Takayama, ‘Pluricanonical systems on algebraic varieties of general type’, Invent. Math. 165 (2006) 551–587.
  • M. Tanabe, ‘Bounds on the number of holomorphic maps of compact Riemann surfaces’, Proc. Amer. Math. Soc. 133 (2005) 3057–3064.
  • H. Tsuji, “Pluricanonical systems of projective varieties of general type II”, Osaka J. Math. 44 (2007), 723–764.