On entire rational maps of real surfaces

In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.


On the sequential order continuity of the C(K)-space
Ercan, Z.; Onal, S. (Springer Science and Business Media LLC, 2007-03-01)
As shown in [1], for each compact Hausdorff space K without isolated points, there exists a compact Hausdorff P'-space X but not an F-space such that C(K) is isometrically Riesz isomorphic to a Riesz subspace of C(X). The proof is technical and depends heavily on some representation theorems. In this paper we give a simple and direct proof without any assumptions on isolated points. Some generalizations of these results are mentioned.
Aytuna, Aydın (Springer Science and Business Media LLC, 1988-9)
We give a characterization of Stein manifolds M for which the space of analytic functions,O(M), is isomorphic as Fréchet spaces to the space of analytic functions on a polydisc interms of the existence of a plurisubharmonic function on M with certain properties. We discuss some corollaries of this result and give some examples.
On equivariant Serre problem for principal bundles
Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2018-08-01)
Let E-G be a Gamma-equivariant algebraic principal G-bundle over a normal complex affine variety X equipped with an action of Gamma, where G and Gamma are complex linear algebraic groups. Suppose X is contractible as a topological Gamma-space with a dense orbit, and x(0) is an element of X is a Gamma-fixed point. We show that if Gamma is reductive, then E-G admits a Gamma-equivariant isomorphism with the product principal G-bundle X x rho E-G(x(0)), where rho : Gamma -> G is a homomorphism between algebraic...
Chirality of real non-singular cubic fourfolds and their pure deformation classification
Finashin, Sergey (Springer Science and Business Media LLC, 2020-02-22)
In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving the hypersurface non-singular. Here, we perform a finer classification giving a full answer to the chirality problem: which of real non-singular cubic hypersurfaces can not be continuously deformed to their mirror reflection.
On symplectic quotients of K3 surfaces
Cinkir, Z; Onsiper, H (Elsevier BV, 2000-12-18)
In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms.
Citation Formats
Y. Ozan, “On entire rational maps of real surfaces,” JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, pp. 77–89, 2002, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37911.