Displaying similar documents to “Bounds for the number of connected components and the first Betti number mod two of a real algebraic surface”

A note on a theorem of Xiao Gang.

Margarita Mendes Lopes (2004)

Collectanea Mathematica

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In 1985 Xiao Gang proved that the bicanonical surface of a complex surface S of general type with p2(S) > 2 is not composed of a pencil. In this note a new proof of this theorem is presented.

Surfaces with prescribed Weingarten operator

Udo Simon, Konrad Voss, Luc Vrancken, Martin Wiehe (2002)

Banach Center Publications

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We investigate pairs of surfaces in Euclidean 3-space with the same Weingarten operator in case that one surface is given as surface of revolution. Our local and global results complement global results on ovaloids of revolution from S-V-W-W.

Timelike Christoffel pairs in the split-quaternions

M. P. Dussan, M. Magid (2010)

Annales Polonici Mathematici

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We characterize the Christoffel pairs of timelike isothermic surfaces in the four-dimensional split-quaternions. When restricting the receiving space to the three-dimensional imaginary split-quaternions, we establish an equivalent condition for a timelike surface in ℝ³₂ to be real or complex isothermic in terms of the existence of integrating factors.

On surface braids of index four with at most two crossings

Teruo Nagase, Akiko Shima (2005)

Fundamenta Mathematicae

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Let Γ be a 4-chart with at most two crossings. We show that if the closure of the surface braid obtained from Γ is one 2-sphere, then the sphere is a ribbon surface.

Lorentzian isothermic surfaces and Bonnet pairs

M. A. Magid (2004)

Annales Polonici Mathematici

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Lorentzian surfaces in Lorentz three-space are studied using an indefinite version of the quaternions. A classification theorem for Bonnet pairs in Lorentz three-space is obtained.

Geometry of some twistor spaces of algebraic dimension one

Nobuhiro Honda (2015)

Complex Manifolds

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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...