Related papers: Moduli Spaces for Dynamical Systems with Portraits

We study constant Q-curvature metrics conformal to the round metric on the sphere with finitely many point singularities. We show that the moduli space of solutions with finitely many punctures in fixed positions, equipped with the…

We construct a metric on the moduli space of bodies in Euclidean space. The moduli space is defined as the quotient space with respect to the action of integral affine transformations. This moduli space contains a subspace, the moduli space…

Consider, in the moduli space of Riemann surfaces of a fixed genus, the subset of surfaces with non-trivial automorphisms. Of special interest are the numerous subsets of surfaces admitting an action of a given finite group, $G$, acting…

Let X be an algebraic curve. We study the problem of parametrizing geometric data over X, which is only generically defined. E.g., parametrizing generically defined (aka rational) maps from X to a fixed target scheme Y. There are three…

We provide a general framework to study convergence properties of families of maps. For manifolds $M$ and $N$ where $M$ is equipped with a volume form $\mathcal{V}$ we consider families of maps in the collection $\{(\phi, B) : B \subset M,…

We prove the existence of global minimal models for rational morphisms $\phi:{\mathbb P}^N\rightarrow{\mathbb P}^N$ of projective space defined over the field of fractions of a principal ideal domain.

We consider the space $\mathcal M$ of ordered quadruples of distinct points in the boundary of complex hyperbolic $n$-space, $\ch{n},$ up to its holomorphic isometry group ${\rm PU}(n,1).$ One of the important problems in complex hyperbolic…

The commutative semiring $\mathbf{D}$ of finite, discrete-time dynamical systems was introduced in order to study their (de)composition from an algebraic point of view. However, many decision problems related to solving polynomial equations…

We show that the moduli space of positive Ricci curvature metrics on all the total spaces of $S^7$-bundles over $S^8$ which are rational homology spheres has infinitely many path components. Furthermore, we carry out the diffeomorphism…

Let M and N be even-dimensional oriented real manifolds, and $u:M \to N$ be a smooth mapping. A pair of complex structures at M and N is called u-compatible if the mapping u is holomorphic with respect to these structures. The quotient of…

For a complex elliptic curve $E$ and a point $p$ of order $n$ on it, the images of the points $p_k=kp$ under the Weierstrass embedding of $E$ into $\mathbb{C}\mathbb{P}^2$ are collinear if and only if the sum of indices is divisible by $n$.…

Let G be a profinite group which is topologically finitely generated, p a prime number and d an integer. We show that the functor from rigid analytic spaces over Q_p to sets, which associates to a rigid space Y the set of continuous…

The main purpose of this paper is to prove the existence of the moduli space parameterizing the embedded curve singularities of $(k^N,0)$ with an admissible Hilbert polynomial and to study its basic properties.

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve; we study the moduli problem of parametrizing certain pairs consisting of a sheaf E on S and a map of E to a fixed reference sheaf on…

We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy transformation around the puncture. We show that under a certain condition on the…

We consider a space $\mathcal{U}$ of 3-dimensional diffeomorphisms $f$ with hyperbolic fixed points $p$ the stable and unstable manifolds of which have quadratic tangencies and satisfying some open conditions and such that $Df(p)$ has…

We investigate deformations of extremal near-horizon geometries in Einstein-Maxwell-Dilaton theory, including various topological terms, and also in D=11 supergravity. By linearizing the field equations and Bianchi identities over the…

Consider the Fulton-MacPherson configuration space of $n$ points on $\P^1$, which is isomorphic to a certain moduli space of stable maps to $\P^1$. We compute the cone of effective ${\mathfrak S}_n$-invariant divisors on this space. This…

Let $G$ be a Lie group, with an invariant metric on its Lie algebra $\mathfrak{g}$. Given a surface $\Sigma$ with boundary, and a collection of base points $\mathcal{V}\subset \Sigma$ meeting every boundary component, the moduli space…