Displaying similar documents to “Computation of Period Matrices of Real Algebraic Curves*”

Some (non-)elimination results for curves in geometric structures

Serge Randriambololona, Sergei Starchenko (2011)

Fundamenta Mathematicae

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We show that the first order structure whose underlying universe is ℂ and whose basic relations are all algebraic subsets of ℂ² does not have quantifier elimination. Since an algebraic subset of ℂ² is either of dimension ≤ 1 or has a complement of dimension ≤ 1, one can restate the former result as a failure of quantifier elimination for planar complex algebraic curves. We then prove that removing the planarity hypothesis suffices to recover quantifier elimination: the structure with...

Algebraic representation formulas for null curves in Sl(2,ℂ)

Hubert Gollek (2005)

Banach Center Publications

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We study curves in Sl(2,ℂ) whose tangent vectors have vanishing length with respect to the biinvariant conformal metric induced by the Killing form, so-called null curves. We establish differential invariants of them that resemble infinitesimal arc length, curvature and torsion of ordinary curves in Euclidean 3-space. We discuss various differential-algebraic representation formulas for null curves. One of them, a modification of the Bianchi-Small formula, gives an Sl(2,ℂ)-equivariant...

On the geometry of algebraic curves having many real components.

J. Huisman (2001)

Revista Matemática Complutense

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We show that there is a large class of nonspecial effective divisors of relatively small degree on real algebraic curves having many real components i.e. on M-curves. We apply to 1. complete linear systems on M-curves containing divisors with entirely real support, and 2. morphisms of M-curves into P1.