The second main theorem for holomorphic curves intersecting hypersurfaces with Casorati determinant into complex projective spaces

Abstract

Abstract. Let f : C → P n (C) be a holomorphic curves with hyperorder strictly less than 1, and algebraically nondegenerate over the field P 1 c which consists of c-periodic meromorphic functions on C. Let {Q j } q j=1 be fixed or c-periodic slowly moving hypersurfaces with degree d j (j ∈ {1, . . . , q}) in (weakly) N -subgeneral position in P n (C). In this paper, we prove a difference version of the second main theorem for f intersecting {Q j } q j=1 by using the Casorati determinant. A difference counterpart of the truncated second main theorem is also obtained. Our results extend the second main theorems for differences with fixed hyperplanes [9] or c-periodic slowly moving hyperplanes [10].

Logarithmic difference lemma in several complex variables and partial difference equations

“…(ii). By the new version of the logarithmic difference lemma, all the second main theorem and Picard type theorem for meromorphic mappings from C m into complex projective spaces P n (C) obtained in [24,1,2] (including also [16,36,25,3]) can be improved under the assumption of (5).…”