## Illinois Journal of Mathematics

### Extension of plurisubharmonic functions in the Lelong class

Ozcan Yazici

#### Abstract

Let $X$ be an algebraic subvariety of $\mathbb{C}^{n}$ and $\overline{X}$ be its closure in $\mathbb{P}^{n}$. In their paper (J. Reine Angew. Math. 676 (2013), 33–49), Coman, Guedj and Zeriahi proved that any plurisubharmonic function with logarithmic growth on $X$ extends to a plurisubharmonic function with logarithmic growth on $\mathbb{C}^{n}$ when the germs $(\overline{X},a)$ in $\mathbb{P}^{n}$ are irreducible for all $a\in\overline{X}\setminus X$. In this paper we consider $X$ for which the germ $(\overline{X},a)$ is reducible for some $a\in\overline{X}\setminus X$ and we give a necessary and sufficient condition for $X$ so that any plurisubharmonic function with logarithmic growth on $X$ extends to a plurisubharmonic function with logarithmic growth on $\mathbb{C}^{n}$.

#### Article information

Source
Illinois J. Math., Volume 58, Number 1 (2014), 219-231.

Dates
First available in Project Euclid: 1 April 2015

https://projecteuclid.org/euclid.ijm/1427897175

Digital Object Identifier
doi:10.1215/ijm/1427897175

Mathematical Reviews number (MathSciNet)
MR3331848

Zentralblatt MATH identifier
1329.32018

#### Citation

Yazici, Ozcan. Extension of plurisubharmonic functions in the Lelong class. Illinois J. Math. 58 (2014), no. 1, 219--231. doi:10.1215/ijm/1427897175. https://projecteuclid.org/euclid.ijm/1427897175

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