Equidistribution in higher codimension for holomorphic endomorphisms of $\mathbb {P}^k$
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Abstract:
In this paper, we discuss the equidistribution phenomena for holomorphic endomorphisms over $\mathbb {P}^k$ in the case of bidegree $(p,p)$ with $1\leq p\leq k$, in particular, $1<p<k$. We prove that if $f:\mathbb {P}^k\to \mathbb {P}^k$ is a holomorphic endomorphism of degree $d\geq 2$ and $T^p$ denotes the Green $(p,p)$-current associated with $f$, then there exists a proper invariant analytic subset $E$ for $f$ such that $d^{-pn}(f^n)^*(S)$ converges to $T^p$ exponentially fast in the current sense for every positive closed $(p,p)$-current $S$ of mass $1$ which is smooth on $E$.References
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Additional Information
- Taeyong Ahn
- Affiliation: Center for Geometry and its Applications, Pohang University of Science and Technology, Pohang City 790-784, The Republic of Korea
- MR Author ID: 1115711
- Email: triumph@postech.ac.kr
- Received by editor(s): March 12, 2014
- Published electronically: May 4, 2015
- Additional Notes: The research of the author was supported in part by SRC-GaiA (Center for Geometry and its Applications), the Grant 2011-0030044 from The Ministry of Education, The Republic of Korea.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3359-3388
- MSC (2010): Primary 37F10, 32H50, 32U40
- DOI: https://doi.org/10.1090/tran/6539
- MathSciNet review: 3451880