Journal of the Mathematical Society of Japan

Log canonical algebras and modules

Caucher BIRKAR

Full-text: Open access

Abstract

Let $(X/Z,B)$ be a lc pair with $K_X+B$ pseudo-effective$/Z$ and $Z$ affine. We show that $(X/Z,B)$ has a good log minimal model if and only if its log canonical algebra and modules are finitely generated.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 4 (2013), 1319-1328.

Dates
First available in Project Euclid: 24 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1382620194

Digital Object Identifier
doi:10.2969/jmsj/06541319

Mathematical Reviews number (MathSciNet)
MR3127825

Zentralblatt MATH identifier
1291.14030

Subjects
Primary: 14E30: Minimal model program (Mori theory, extremal rays)

Keywords
minimal models log canonical algebra finite generation

Citation

BIRKAR, Caucher. Log canonical algebras and modules. J. Math. Soc. Japan 65 (2013), no. 4, 1319--1328. doi:10.2969/jmsj/06541319. https://projecteuclid.org/euclid.jmsj/1382620194


Export citation

References

  • C. Birkar, On existence of log minimal models and weak Zariski decompositions, Math. Ann., 354 (2012), 787–799.
  • C. Birkar, P. Cascini, C. Hacon and J. McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., 23 (2010), 405–468.
  • J.-P. Demailly, C. D. Hacon and M. Păun, Extension theorems, Non-vanishing and the existence of good minimal models, Acta Math., 210 (2013), 203–259.
  • R. Hartshorne, Generalized divisors on Gorenstein schemes, $K$-theory, 8 (1994), 287–339.
  • J. Kollár and S. Mori, Birational Geometry of Algebraic Varieties, Cambridge Tracts in Math., 134, Cambridge University Press, 1998.
  • N. Nakayama, Zariski-decomposition and Abundance, MSJ Memoirs, 14, Math. Soc. Japan, Tokyo, 2004.