Kaliman, Shulim Exotic analytic structures and Eisenman intrinsic measures. (English) Zbl 0821.14025 Isr. J. Math. 88, No. 1-3, 411-423 (1994). Author’s abstract: “Using Eisenman intrinsic measures we prove a cancellation theorem. This theorem allows to find new examples of exotic analytic structures on \(\mathbb{C}^ n\) under which we understand smooth complex affine algebraic varieties which are diffeomorphic to \(\mathbb{R}^{2n}\) but not biholomorphic to \(\mathbb{C}^ n\). We also develop a new method of constructing these structures with a given number of hypersurfaces isomorphic to \(\mathbb{C}^ 2\) and a family of these structures with a given number of moduli”. Reviewer: N.Mihalache (Bucureşti) Cited in 1 ReviewCited in 13 Documents MSC: 14J10 Families, moduli, classification: algebraic theory 14J15 Moduli, classification: analytic theory; relations with modular forms 32G05 Deformations of complex structures Keywords:cancellation theorem; exotic analytic structures; number of moduli PDF BibTeX XML Cite \textit{S. Kaliman}, Isr. J. Math. 88, No. 1--3, 411--423 (1994; Zbl 0821.14025) Full Text: DOI References: [1] [D] A. Dimca,Hypersurfaces in C 2n diffeomorphic to R 4n-2 (n), Max-Plank Institute, preprint, 1990. [2] [E] D. A. Eisenman,Intrinsic measures on complex manifolds and holomorphic mappings, Mem. AMS, No. 96, AMS, Providence, R.I., 1970. · Zbl 0197.05901 [3] [FZ] H. Flenner and M. Zaidenberg,Q-acyclic surfaces and their deformations, preprint, 1992. [4] [F] T. Fujita,On the topology of non-complete algebraic surfaces, J. Fac. Sci. Univ. Tokyo (ser. 1A)29 (1982), 503–566. · Zbl 0513.14018 [5] [GW] I. Graham and H. Wu,Some remarks on the intrinsic measures of Eisenman, Trans. AMS288 (1985), 625–660. · Zbl 0582.32034 · doi:10.1090/S0002-9947-1985-0776396-4 [6] [IF] S. Iitaka and T. Fujita,Cancellation theorem for algebraic varieties. J. Fac. Sci. Univ. Tokyo (Sec. 1A)24 (1977), 123–127. · Zbl 0353.14013 [7] [Ka] S. Kaliman,Smooth contractible hypersurfaces in C n and exotic algebraic structures on C 3, Math. Zeitschrift (to appear). [8] [Ko] S. Kobayashi,Intrinsic distances, measures and geometric function theory, Bull. AMS82 (1976), 357–416. · Zbl 0346.32031 · doi:10.1090/S0002-9904-1976-14018-9 [9] [NS] T. Nishino and M. Suzuki,Sur les singularités essentielles et isolées des applications holomorphes á valeuers dans une surface complexe, Publ. RIMS, Kyoto Univ.16 (1980), 461–497. · Zbl 0506.32007 · doi:10.2977/prims/1195187213 [10] [PtD] T. Petrie and T. tom Dieck,Contractible affine surfaces of Kodaira dimension one, Japan. J. Math.16 (1990), no. 1, 147–169. · Zbl 0721.14018 [11] [R] C. P. Ramanujam,A topological characterization of the affine plane as an algebraic variety, Ann. Math.94 (1971), 69–88. · Zbl 0218.14021 · doi:10.2307/1970735 [12] [Ru] P. Russell,On a class of C 3-like threefolds, Preliminary report, 1992. [13] [Sa] F. Sakai,Kodaira dimension of complement of divisor, inComplex Analysis and Algebraic Geometry, Iwanami, Tokyo, 1977, pp. 239–257. [14] [T] R. Tsushima,Rational maps of varieties of hyperbolic type, Proc. Japan Acad. (Ser. A)22 (1979), 95–100. · Zbl 0443.14006 · doi:10.3792/pjaa.55.95 [15] [W] J. Winkelmann,On free holomorphic C *-action on C n and homogeneous Stein manifolds, Math. Ann.286 (1990), 593–612. · Zbl 0708.32004 · doi:10.1007/BF01453590 [16] [Z1] M. Zaidenberg,Analytic cancellation theorem and exotic algebraic structures on C n ,n, Max-Planck-Institut für Mathematik, Bonn, preprint MPI/91-26, 33p, 1991. [17] [Z2] M. Zaidenberg,Ramanujam surfaces and exotic algebraic structures on C n , Dokl. AN SSSR314 (1990), 1303–1307; English transl. in Soviet Math. Doklady42 (1991), 636–640. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.