Kyoto Journal of Mathematics

A remark on Kovács’s vanishing theorem

Osamu Fujino

Full-text: Open access


We give an alternative proof of Kovács’s vanishing theorem. Our proof is based on the standard arguments of the minimal model theory. We do not need the notion of Du Bois pairs. We reduce Kovács’s vanishing theorem to the well-known relative Kawamata–Viehweg–Nadel vanishing theorem.

Article information

Kyoto J. Math., Volume 52, Number 4 (2012), 829-832.

First available in Project Euclid: 15 November 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F17: Vanishing theorems [See also 32L20]
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)


Fujino, Osamu. A remark on Kovács’s vanishing theorem. Kyoto J. Math. 52 (2012), no. 4, 829--832. doi:10.1215/21562261-1728884.

Export citation


  • [F1] O. Fujino, Semi-stable minimal model program for varieties with trivial canonical divisor, Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), 25–30.
  • [F2] O. Fujino, On isolated log canonical singularities with index one, J. Math. Sci. Univ. Tokyo 18 (2011), 299–323.
  • [F3] O. Fujino, Introduction to the log minimal model program for log canonical pairs, preprint, 2009.
  • [F4] O. Fujino, Vanishing theorems, preprint, 2011.
  • [Ko] J. Kollár, Lectures on resolution of singularities, Ann. of Math. Stud. 166, Princeton Univ. Press, Princeton, 2007.
  • [Kv] S. J. Kovács, Du Bois pairs and vanishing theorems, Kyoto J. Math. 51 (2011), 47–69.