Sums of squares on real algebraic curves

2003 ◽  
Vol 245 (4) ◽  
pp. 725-760 ◽  
Author(s):  
Claus Scheiderer
Keyword(s):  
Algebraic Curves ◽  
Sums Of Squares ◽  
Real Algebraic Curves

scholarly journals Double coverings of hyperelliptic real algebraic curves

2008 ◽  
Vol 212 (9) ◽  
pp. 2011-2026
Author(s):  
E. Bujalance ◽  
F.J. Cirre ◽  
J.M. Gamboa
Keyword(s):  
Algebraic Curves ◽  
Real Algebraic Curves ◽  
Double Coverings

scholarly journals N=2 supersymmetric kinks and real algebraic curves

2000 ◽  
Vol 480 (3-4) ◽  
pp. 373-380 ◽  
Author(s):  
A. Alonso Izquierdo ◽  
M.A. González León ◽  
J. Mateos Guilarte
Keyword(s):  
Algebraic Curves ◽  
Real Algebraic Curves

scholarly journals SIGNATURES OF COLORED LINKS WITH APPLICATION TO REAL ALGEBRAIC CURVES

2005 ◽  
Vol 14 (07) ◽  
pp. 883-918 ◽  
Author(s):  
V. FLORENS
Keyword(s):  
Algebraic Curves ◽  
Betti Numbers ◽  
Alexander Polynomial ◽  
Necessary Condition ◽  
Oriented Link ◽  
Real Algebraic Curves

We construct the signature of a μ-colored oriented link, as a locally constant integer valued function with domain (S1 - {1})μ. It restricts to the Tristram–Levine's signature on the diagonal and the discontinuities can occur only at the zeros of the colored Alexander polynomial. Moreover, the signature and the related nullity verify the Murasugi–Tristram inequality. This gives a new necessary condition for a link to bound a smoothly and properly embedded surface in B4, with given Betti numbers. As an application, we achieve the classification of the complex orientations of maximal plane non-singular projective algebraic curves of degree 7, up to isotopy.

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