On the holomorphic closure dimension of real analytic sets
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- by Janusz Adamus and Rasul Shafikov PDF
- Trans. Amer. Math. Soc. 363 (2011), 5761-5772 Request permission
Abstract:
Given a real analytic (or, more generally, semianalytic) set $R$ in $\mathbb {C}^n$ (viewed as $\mathbb {R}^{2n}$), there is, for every $p\in \bar {R}$, a unique smallest complex analytic germ $X_p$ that contains the germ $R_p$. We call $\dim _{\mathbb {C}}X_p$ the holomorphic closure dimension of $R$ at $p$. We show that the holomorphic closure dimension of an irreducible $R$ is constant on the complement of a closed proper analytic subset of $R$, and we discuss the relationship between this dimension and the CR dimension of $R$.References
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Additional Information
- Janusz Adamus
- Affiliation: Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7 – and – Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland
- Email: jadamus@uwo.ca
- Rasul Shafikov
- Affiliation: Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7
- MR Author ID: 662426
- Email: shafikov@uwo.ca
- Received by editor(s): June 3, 2008
- Received by editor(s) in revised form: April 3, 2009, and September 17, 2009
- Published electronically: June 9, 2011
- Additional Notes: This research was partially supported by the Natural Sciences and Engineering Research Council of Canada.
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 5761-5772
- MSC (2010): Primary 32B20, 32V40
- DOI: https://doi.org/10.1090/S0002-9947-2011-05276-1
- MathSciNet review: 2817408