Results 21 to 30 of about 574 (169)
Birational self-maps of threefolds of (un)-bounded genus or gonality [PDF]
, 2022 We study the complexity of birational self-maps of a projective threefold X by looking at the birational type of surfaces contracted. These surfaces are birational to the product of the projective line with a smooth projective curve.
Blanc, Jérémy +6 more
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Periodic Orbits of Planar Integrable Birational Maps [PDF]
, 2015 A birational planar map F possessing a rational first integral preserves a foliation of the plane given by algebraic curves which, if F is not globally periodic, is given by a foliation of curves that have generically genus 0 or 1.
Víctor Mañosa +3 more
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ON THE DYNAMICS OF BIRATIONAL MAPPINGS OF THE PLANE [PDF]
Journal of the Korean Mathematical Society, 2003 Summary: In this paper we discuss how the dynamics of certain birational maps of the real plane may be studied using complex methods.
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On the moduli space of superminimal surfaces in spheres
International Journal of Mathematics and Mathematical Sciences, 2003 Using a birational correspondence between the twistor space of S2n and projective space, we describe, up to birational equivalence, the moduli space of superminimal surfaces in S2n of degree d as curves of degree d in projective space satisfying a ...
Luis Fernández
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Integrable maps in 4D and modified Volterra lattices [PDF]
Open Communications in Nonlinear Mathematical PhysicsIn recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus $g$. As well as proving that each such discrete system is
A. N. W. Hone +3 more
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Effective criteria for bigraded birational maps
Journal of Symbolic Computation, 2017 In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices.
Nicolás Botbol +5 more
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Degree growth of birational maps of the plane
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2015 This article studies the sequence of iterative degrees of a birational map of the plane. This sequence is known either to be bounded or to have a linear, quadratic or exponential growth. The classification elements of infinite order with a bounded sequence of degrees is achieved, the case of elements of finite order being already known.
Déserti, Julie, Blanc, Jérémy
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Entropy of meromorphic maps and dynamics of birational maps [PDF]
Mémoires de la Société mathématique de France, 2010 We study the dynamics of meromorphic maps for a compact Kaehler manifold X. More precisely, we give a simple criterion that allows us to produce a measure of maximal entropy. We can apply this result to bound the Lyapunov exponents. Then, we study the particular case of a family of generic birational maps of P^k for which we construct the Green ...
de Thélin, Henry, Vigny, Gabriel
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On Quadrirational Yang-Baxter Maps
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This
V.G. Papageorgiou +3 more
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Energy and invariant measures for birational surface maps [PDF]
Duke Mathematical Journal, 2005 When a birational surface map is expanding on cohomology there is a canonical way to associate positive closed currents to the map and its inverse. In this paper we use a version of Dirichlet energy to construct the wedge product of these two currents under a very weak additional condition on the map. We show that the resulting measure is invariant and
Bedford, Eric, Diller, Jeffrey
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