Proceedings of the Japan Academy, Series A, Mathematical Sciences

Remarks on the abundance conjecture

Kenta Hashizume

Full-text: Open access

Abstract

We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical 4-folds.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 9 (2016), 101-106.

Dates
First available in Project Euclid: 2 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.pja/1478052014

Digital Object Identifier
doi:10.3792/pjaa.92.101

Mathematical Reviews number (MathSciNet)
MR3567594

Zentralblatt MATH identifier
1365.14019

Subjects
Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14J35: $4$-folds

Keywords
Abundance theorem big boundary divisor good minimal model finite generation of adjoint ring

Citation

Hashizume, Kenta. Remarks on the abundance conjecture. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 9, 101--106. doi:10.3792/pjaa.92.101. https://projecteuclid.org/euclid.pja/1478052014


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