Displaying similar documents to “Rational real algebraic models of topological surfaces.”

Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

Andrey Trepalin (2014)

Open Mathematics

Similarity:

Let 𝕜 be a field of characteristic zero and G be a finite group of automorphisms of projective plane over 𝕜 . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field 𝕜 is algebraically closed. In this paper we prove that ℙ 𝕜 2 ℙ 𝕜 2 G G is rational for an arbitrary field 𝕜 of characteristic zero.

On triple curves through a rational triple point of a surface

M. R. Gonzalez-Dorrego (2006)

Annales Polonici Mathematici

Similarity:

Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.

Approximation of holomorphic maps by algebraic morphisms

J. Bochnak, W. Kucharz (2003)

Annales Polonici Mathematici

Similarity:

Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.

Geometry of some twistor spaces of algebraic dimension one

Nobuhiro Honda (2015)

Complex Manifolds

Similarity:

It is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is...