{'fraction_non_alphanumeric': 0.02579132473622509, 'fraction_numerical': 0.0, 'mean_word_length': 4.809523809523809, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
NONPROPER INTERSECTION THEORY AND POSITIVE CURRENTS I, LOCAL ASPECTS

We introduce a current calculus to deal with (local) non-proper in- tersection theory, especially construction of local cycles of Stuckrad-Vogel type (Vogel cycles). Given a coherent ideal sheaf J, generated by a tuple of functions f semiglobally on a reduced analytic space X, we construct a current M f , ob- tained as a limit of explicit expressions in f, whose Lelong numbers at each point of its components of various bidegrees are precisely the Segre numbers associated to J at the point. The precise statement is a generalization of the classical King formula. The current M f can be interpreted, at each point, as a mean value of various local Vogel cycles. Our current calculus also admits a convenient approach to Tworzewski's locally defined invariant intersection theory.