相关论文: Remarks on quadratic rational maps
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…
We present a natural extension of the notion of nondegenerate rational maps (quadrirational maps) to arbitrary dimensions. We refer to these maps as $2^n-$rational maps. In this note we construct a rich family of $2^n-$rational maps. These…
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
We discuss some examples of geometrically meaningful rational self-maps of moduli space of curves of low genus and homogeneous forms.
We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…
We study the space of real rational curves of low degree in the quadric of signature $(3,2)$ and provides a classificaton of real rational knots and nodal curves. Apart from the classification, we also study the relationship between the…
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…
We study the group of self-equivalences of a partially postcritically finite branched cover and answer a question of Adam Epstein about contractibility of certain deformation spaces of rational maps.
We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a…
The Fatou-Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to…
This is a preliminary investigation of the geometry and dynamics of rational maps with only two critical points. (originally titled ``On Bicritical Rational Maps'' in September 1997; revised and retitled April 1999)
The Epstein deformation space parameterizes marked rational maps with prescribed combinatorial and dynamical structure. For the family of quadratic rational maps with a periodic critical cycle of order 4 and an extra critical point not…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We continue the study of constructing invariant Laplacians on Julia sets, and studying properties of their spectra. In this paper we focus on two types of examples: 1) Julia sets of cubic polynomials $z^3 + c$ with a single critical point;…
We study rationality constructions for smooth complete intersections of two quadrics over nonclosed fields. Over the real numbers, we establish a criterion for rationality in dimension four.
In this paper, we consider the family of rational maps $$\F(z) = z^n + \frac{\la}{z^d},$$ where $n \geq 2$, $d\geq 1$, and$\la \in \bbC$. We consider the case where $\la$ lies in the main cardioid of one of the $n-1$ principal Mandelbrot…
The notion of quadratic maps between arbitrary groups appeared at several places in the literature on quadratic algebra. Here a unified extensive treatment of their properties is given; the relation with a relative version of Passi's…
We introduce a notion of $R$-quadratic maps between modules over a commutative ring $R$ which generalizes several classical notions arising in linear algebra and group theory. On a given module $M$ such maps are represented by $R$-linear…
We give a conjectural formula for the characteristic number of rational cuspidal curves in the projective plane by extending the idea of Kontsevich's recursion formula (namely, pulling back the equality of two divisors in the four pointed…
Given a projective intersection of two quadrics X in at least 9 variables, the quantitative behaviour of the rational points on X is investigated under the assumption that X contains a pair of conjugate singular points defined over the…