Displaying similar documents to “Surfaces in 3-space that do not lift to embeddings in 4-space”

A note on a theorem of Xiao Gang.

Margarita Mendes Lopes (2004)

Collectanea Mathematica


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.

On surface braids of index four with at most two crossings

Teruo Nagase, Akiko Shima (2005)

Fundamenta Mathematicae


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.

The irregularity of ruled surfaces in three dimensional projective space.

Luis Giraldo, Ignacio Sols (1998)

Collectanea Mathematica


Let S be a ruled surface in P3 with no multiple generators. Let d and q be nonnegative integers. In this paper we determine which pairs (d,q) correspond to the degree and irregularity of a ruled surface, by considering these surfaces as curves in a smooth quadric hypersurface in P5.

Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants

Alex Eskin, Howard Masur, Anton Zorich (2003)

Publications Mathématiques de l'IHÉS


A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of conical points one can find with a nonzero probability another saddle connection on S having the same direction and the same length as the initial one. A similar phenomenon is valid for the families of parallel closed geodesics. We give a complete description...