### Bounds for the number of connected components and the first Betti number mod two of a real algebraic surface

R. Silhol (1986)

Compositio Mathematica

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R. Silhol (1986)

Compositio Mathematica

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Vo Van Tan (1989)

Compositio Mathematica

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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.

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.

G. Lucca (2003)

Visual Mathematics

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Brakke, Kenneth A. (1992)

Experimental Mathematics

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Balan, Vladimir, Vîlcea, Ştefania-Alina (2005)

Balkan Journal of Geometry and its Applications (BJGA)

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Alois Švec (1989)

Czechoslovak Mathematical Journal

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Joets, Alain, Ribotta, Roland (1999)

Experimental Mathematics

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Martin Bright (2011)

Acta Arithmetica

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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.