Title: On the holomorphic closure dimension of real analytic sets
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 $X_p$ t...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 $R$.Read More