2. Mark the third intersection of the vertical line and the elliptic curve as -R, which will be the infinity point of the 2-dimensional space. This is where the vertical line and the elliptic curve will eventually intersect. In other words, -R is the infinity point: ...
Li, "Critical groups at infinity, saddle point reduction and elliptic resonant problems," Communications in Contemporary Mathematics, vol. 5, no. 5, pp. 761-773, 2003.Liu, S., Li, S.: Critical groups at infinity, saddle point reduction and elliptic reso- nant problems. Commun. Contemp. ...
complex polynomials in one variable, of degreenand with distinct roots. In this way braids offer a close connection between algebraic geometry and topology. In this paper we illustrate how this connection is beneficial in both directions. We use topological arguments to prove that there exist...
The singu- lar foliation has two types of singularities; elliptic singularities, which are the roots of p, and hyperbolic singularities, which are the critical points of p. Every singular leaf of this foliation has the shape of a cross, consisting of one line connecting two roots of p and ...
Instanton Geometry and Quantum A-infinity structure on the Elliptic Curve We first determine and then study the complete set of non-vanishing A-model correlation functions associated with the ``long-diagonal branes'' on the ellip... M Herbst,W Lerche,D Nemeschansky - High Energy Physics - ...
A hyperelliptic curve over Q is called "locally soluble" if it has a point over every completion of Q. In this paper, we prove that a positive proportion of hyperelliptic curves over Q of genus g≥1 are locally soluble but have no points over any odd degree extension of Q. We also ...
1.24. In this case, the lift curve has two approximately straight portions, of different slopes. The slope of the lower portion is almost the same as that for a thicker section, but, at a moderate incidence, it takes a different, smaller value, leading to a smaller value ofCLmax, ...
Li, "Critical groups at infinity, saddle point reduction and elliptic resonant problems," Communications in Contemporary Mathematics, vol. 5, no. 5, pp. 761-773, 2003.Liu, S., Li, S.: Critical groups at infinity, saddle point reduction and elliptic reso- nant problems. Commun. Contemp. ...
Starting with κ 1 small to the very right of the curve, equilibria are stable until we reach the first maximum of Mκ at the point A (the "white dwarf" region). This is consistent with the statement of Theorem 1.13, which if applicable to this equation of state would imply that the...
The solution of the Bethe equations in this limit is described by a Riemann surface with a finite number of cuts.28 The general finite zone solution in the su(2) sector is described by a hyperelliptic complex curve [87]. 6.1 Scalar products and norms in the semi-classical limit An N ...