![]() Our contributors are asked to make sure their submissions comply with rules governing the formatting. Communications and Rapid Communications.written in English - attention to detail of the language will avoid severe misunderstandings which might lead to rejection of the paper.be clearly and correctly written - should contain all essential features of a scientific publication that is easy to understand for the target audience.focus on the aims and scope of the journal.contain original work - not published elsewhere in any medium (in the whole or in part) by the authors or anyone else and not under consideration for publication in any other medium.In case of problems, please contact the Editorial Office of this journal at submitted to this journal should: Manuscripts should be submitted to the journal via online submission system Editorial Manager available for this journal at. ![]() In particular, we obtain a linear differential system of order lower than that of the Gelfand-Gindikin-Graev differential system, characterizing the images by the Chow transformation of smooth differential forms on the complex projective space. This is a consequence of the existence of dual currents, defined on the dual complex projective space. ![]() Then, the proofs can be simplified by using the conormal currents, which exist for all currents of bidimension ( p, p ) \left(p,p) on the complex projective space, even not closed. This integral transformation is a factor of a left inverse of the Chow transformation and its composition with the Chow transformation is a right inverse of a linear differential operator, which does not commute with ∂ \partial or ∂ ¯ \overline -modules of the properties of the Chow transformation. We define a dual of the Chow transformation of currents on any complex projective manifold. We also provide several examples of such complex surfaces including triple points, which are smoothable to K 3 K3 surfaces. As an application, we provide several examples of d d -semistable SNC complex surfaces with trivial canonical bundle including double curves, which are smoothable to complex tori, primary Kodaira surfaces, and K 3 K3 surfaces. ![]() In particular, these volume forms are given as solutions of a nonlinear elliptic partial differential equation. The proof is based on an explicit construction of local smoothings around the singular locus of X X, and the first author’s existence result of holomorphic volume forms on global smoothings of X X. This can be interpreted as a differential geometric analogue of the smoothability results due to Friedman, Kawamata-Namikawa, Felten-Filip-Ruddat, Chan-Leung-Ma, and others in algebraic geometry. We prove that if X X is d d -semistable, then there exists a family of smoothings in a differential geometric sense. Let X X be a simple normal crossing (SNC) compact complex surface with trivial canonical bundle which includes triple intersections. Inquiries concerning APCs should be addressed before or immediately after submission of a paper to the Editorial Office ( are NO submission charges. For more details please check Article Processing Charges.Īuthors with limited access to funds, may request for a discount or a waiver. Article Processing Charges will apply after the acceptance of a manuscript. Since 2021 articles published in the COMA are subject to a voluntary Article Processing Charge (APC).
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