Displaying similar documents to “Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel-Veech constants”

Surfaces in 3-space that do not lift to embeddings in 4-space

J. Carter, Masahico Saito (1998)

Banach Center Publications

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A necessary and sufficient condition for an immersed surface in 3-space to be lifted to an embedding in 4-space is given in terms of colorings of the preimage of the double point set. Giller's example and two new examples of non-liftable generic surfaces in 3-space are presented. One of these examples has branch points. The other is based on a construction similar to the construction of Giller's example in which the orientation double cover of a surface with odd Euler characteristic...

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.

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.

Equations defining reducible Kummer surfaces in ℙ⁵

Tomasz Szemberg (1996)

Annales Polonici Mathematici

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Principally polarized abelian surfaces are the Jacobians of smooth genus 2 curves or of stable genus 2 curves of special type. In [S] we studied equations describing Kummer surfaces in the case of an irreducible principal polarization on the abelian surface. The aim of this note is to give a treatment of the second case. We describe intermediate Kummer surfaces coming from abelian surfaces carrying a product principal polarization. In Proposition 12 we give explicit equations of these...