Algebra & Number Theory

A fibered power theorem for pairs of log general type

Kenneth Ascher and Amos Turchet

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/ant.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let f : (X,D) B be a stable family with log canonical general fiber. We prove that, after a birational modification of the base B˜ B, there is a morphism from a high fibered power of the family to a pair of log general type. If in addition the general fiber is openly canonical, then there is a morphism from a high fibered power of the original family to a pair openly of log general type.

Article information

Source
Algebra Number Theory, Volume 10, Number 7 (2016), 1581-1600.

Dates
Received: 1 March 2016
Revised: 30 June 2016
Accepted: 31 July 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842569

Digital Object Identifier
doi:10.2140/ant.2016.10.1581

Mathematical Reviews number (MathSciNet)
MR3554241

Zentralblatt MATH identifier
1376.14035

Subjects
Primary: 14J10: Families, moduli, classification: algebraic theory
Secondary: 14J29: Surfaces of general type 14E99: None of the above, but in this section 14G05: Rational points

Keywords
log general type moduli of stable pairs Lang–Vojta

Citation

Ascher, Kenneth; Turchet, Amos. A fibered power theorem for pairs of log general type. Algebra Number Theory 10 (2016), no. 7, 1581--1600. doi:10.2140/ant.2016.10.1581. https://projecteuclid.org/euclid.ant/1510842569


Export citation

References

  • D. Abramovich, “A high fibered power of a family of varieties of general type dominates a variety of general type”, Invent. Math. 128:3 (1997), 481–494.
  • D. Abramovich, “Uniformity of stably integral points on elliptic curves”, Invent. Math. 127:2 (1997), 307–317.
  • D. Abramovich and B. Hassett, “Stable varieties with a twist”, pp. 1–38 in Classification of algebraic varieties, European Mathematical Society, Zürich, 2011.
  • D. Abramovich and K. Matsuki, “Uniformity of stably integral points on principally polarized abelian varieties of dimension $\le2$”, Israel J. Math. 121 (2001), 351–380.
  • D. Abramovich and J. F. Voloch, “Lang's conjectures, fibered powers, and uniformity”, New York J. Math. 2 (1996), 20–34, electronic.
  • B. Bhatt, W. Ho, Z. Patakfalvi, and C. Schnell, “Moduli of products of stable varieties”, Compos. Math. 149:12 (2013), 2036–2070.
  • L. Caporaso, J. Harris, and B. Mazur, “Uniformity of rational points”, J. Amer. Math. Soc. 10:1 (1997), 1–35.
  • O. Fujino, “Semipositivity theorems for moduli problems”, preprint, 2012.
  • R. Hartshorne, “Stable reflexive sheaves”, Math. Ann. 254:2 (1980), 121–176.
  • B. Hassett, “Correlation for surfaces of general type”, Duke Math. J. 85:1 (1996), 95–107.
  • B. Hassett and S. J. Kovács, “Reflexive pull-backs and base extension”, J. Algebraic Geom. 13:2 (2004), 233–247.
  • H. Hironaka, “Idealistic exponents of singularity”, pp. 52–125 in Algebraic geometry (J. J. Sylvester Symposium (1976)), edited by J.-I. Igusa, Johns Hopkins University Press, Baltimore, MD, 1977.
  • K. Karu, Semistable reduction in characteristic 0, Ph.D. thesis, Boston University, 1999, hook http://search.proquest.com/docview/304512245/ \posturlhook.
  • J. Kollár, “Book on moduli of surfaces”, book in progress, 2010, hook https://web.math.princeton.edu/~kollar/ \posturlhook.
  • J. Kollár, Singularities of the minimal model program, Cambridge Tracts in Mathematics 200, Cambridge University Press, 2013.
  • J. Kollár and S. J. Kovács, “Log canonical singularities are Du Bois”, J. Amer. Math. Soc. 23:3 (2010), 791–813.
  • J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics 134, Cambridge University Press, 1998.
  • S. J. Kovács and Z. Patakfalvi, “Projectivity of the moduli space of stable log-varieties and subadditvity of log-Kodaira dimension”, preprint, 2015.
  • P. L. Pacelli, “Uniform boundedness for rational points”, Duke Math. J. 88:1 (1997), 77–102.
  • P. L. Pacelli, “Uniform bounds for stably integral points on elliptic curves”, Proc. Amer. Math. Soc. 127:9 (1999), 2535–2546.
  • Z. Patakfalvi, “Fibered stable varieties”, Trans. Amer. Math. Soc. 368:3 (2016), 1837–1869.
  • Z. Patakfalvi and C. Xu, “Ampleness of the CM line bundle on the moduli space of canonically polarized varieties”, preprint, 2015.