Results 11 to 20 of about 99,903 (246)
Invariant algebraic curves for Liénard dynamical systems revisited [PDF]
Applied Mathematics Letters, 2018 A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in $\mathbb{C}^2$ is introduced. The structure of irreducible invariant algebraic curves for Li nard dynamical systems $x_t=y$, $y_t=-g(x)y-f(x)$ with $\text{deg} f=\text{deg} g+1$ is obtained.
Maria Demina
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Hall algebras and curve-counting invariants [PDF]
Journal of the American Mathematical Society, 2011 We use Joyce’s theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants and that the generating functions for these invariants are Laurent expansions of rational functions.
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Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams [PDF]
, 2015 This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus
Hauenstein, Jonathan D. +3 more
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The Yang-Baxter equation for PT invariant nineteen vertex models [PDF]
, 2010 We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry.
Alcaraz F C +12 more
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Invariants of algebraic curves and topological expansion [PDF]
Communications in Number Theory and Physics, 2007 For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the curve becomes singular.
Eynard, Bertrand, Orantin, Nicolas
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Gopakumar-Vafa invariants do not determine flops [PDF]
, 2017 Two 3-fold flops are exhibited, both of which have precisely one flopping curve. One of the two flops is new, and is distinct from all known algebraic D4-flops.
Brown, Gavin, Wemyss, Michael
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Characteristic Number: Theory and Its Application to Shape Analysis
Axioms, 2014 Geometric invariants are important for shape recognition and matching. Existing invariants in projective geometry are typically defined on the limited number (e.g., five for the classical cross-ratio) of collinear planar points and also lack the ability ...
Xin Fan +5 more
doaj +1 more source
Intersection of valuation rings in $k[x,y]$ [PDF]
, 2014 We associate to any given finite set of valuations on the polynomial ring in two variables over an algebraically closed field a numerical invariant whose positivity characterizes the case when the intersection of their valuation rings has maximal ...
Xie, Junyi
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Invariant hypercomplex structures and algebraic curves
Mathematische Nachrichten, 2022 AbstractWe show that ‐invariant hypercomplex structures on (open subsets) of regular semisimple adjoint orbits in correspond to algebraic curves C of genus , equipped with a flat projection of degree k, and an antiholomorphic involution covering the antipodal map on .
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Typical dynamics of plane rational maps with equal degrees [PDF]
, 2016 Let $f:\mathbb{CP}^2\dashrightarrow\mathbb{CP^2}$ be a rational map with algebraic and topological degrees both equal to $d\geq 2$. Little is known in general about the ergodic properties of such maps.
Diller, Jeffrey +2 more
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