Fundamental groups of some special quadric arrangements.

Meirav Amram; Mina Teicher

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Displaying similar documents to “Fundamental groups of some special quadric arrangements.”

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These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009. This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective...

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A real polynomial P of degree n in one real variable is hyperbolic if its roots are all real. A real-valued function P is called a hyperbolic polynomial-like function (HPLF) of degree n if it has n real zeros and P⁽ⁿ⁾ vanishes nowhere. Denote by x_k ⁽ⁱ⁾ the roots of P⁽ⁱ⁾, k = 1, ..., n-i, i = 0, ..., n-1. Then in the absence of any equality of the form x_i...

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Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle O(1), which deforms to a principally polarized Abelian variety, then O(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.