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Reference.org
Complex analytic variety
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, particularly <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a> and <a href="/facts/Complex_geometry/ekCsxAXb">complex geometry</a>, a complex analytic variety or complex analytic space is a generalization of a <a href="/facts/Complex_manifold/DlvPnpzm">complex manifold</a> that allows the presence of <a href="/facts/Singularity_theory/MgLkyrhl">singularities</a>. Complex analytic varieties are <a href="/facts/Locally_ringed_space/JyeaTMtX">locally ringed spaces</a> that are locally isomorphic to local model spaces, where a local model space is an open subset of the vanishing locus of a finite set of <a href="/facts/Holomorphic_function/kVzthtEf">holomorphic functions</a>. </p>