scholarly journals Principal bundles over a real algebraic curve

2012 ◽  
Vol 20 (5) ◽  
pp. 957-988 ◽  
Author(s):  
Indranil Biswas ◽  
Jacques Hurtubise
Keyword(s):  
Algebraic Curve ◽  
Principal Bundles ◽  
Real Algebraic Curve

Super Real Algebraic Curve

2004 ◽  
pp. 396-396
Author(s):  
Yolanda Lozano ◽  
Steven Duplij ◽  
Malte Henkel ◽  
Malte Henkel ◽  
Euro Spallucci ◽  
...  
Keyword(s):  
Algebraic Curve ◽  
Real Algebraic Curve

scholarly journals The topological configuration of a real algebraic curve

1991 ◽  
Vol 43 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Takis Sakkalis
Keyword(s):  
Morse Theory ◽  
Algebraic Curve ◽  
Running Time ◽  
Real Algebraic Curve ◽  
Maximum Coefficient ◽  
Topological Configuration

This paper presents an algorithm, motivated by Morse Theory, for the topological configuration of the components of a real algebraic curve {f(x, y) = 0}. The running time of the algorithm is O(n12 (d + log n)2 log n), where n, d are the degree and maximum coefficient size of f(x, y).

scholarly journals The moduli space of stable vector bundles over a real algebraic curve

2009 ◽  
Vol 347 (1) ◽  
pp. 201-233 ◽  
Author(s):  
Indranil Biswas ◽  
Johannes Huisman ◽  
Jacques Hurtubise
Keyword(s):  
Moduli Space ◽  
Algebraic Curve ◽  
Vector Bundles ◽  
Stable Vector Bundles ◽  
Real Algebraic Curve

scholarly journals The number of connected components of certain real algebraic curves

2001 ◽  
Vol 25 (11) ◽  
pp. 693-701
Author(s):  
Seon-Hong Kim
Keyword(s):  
Algebraic Curve ◽  
Algebraic Curves ◽  
Connected Components ◽  
Connected Component ◽  
The Real ◽  
Real Algebraic Curves ◽  
Real Algebraic Curve

For an integern≥2, letp(z)=∏k=1n(z−αk)andq(z)=∏k=1n(z−βk), whereαk,βkare real. We find the number of connected components of the real algebraic curve{(x,y)∈ℝ2:|p(x+iy)|−|q(x+iy)|=0}for someαkandβk. Moreover, in these cases, we show that each connected component contains zeros ofp(z)+q(z), and we investigate the locus of zeros ofp(z)+q(z).

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