Related papers: The Ramificant Determinant
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…
Let $C$ be an irreducible algebraic curve defined over a number field and inside an algebraic torus of dimension at least 3. We partially answer a question posed by Levin on points on $C$ for which a non-trivial power lies again on $C$. Our…
We construct moduli spaces of framed logarithmic connections and also moduli spaces of framed parabolic connections. It is shown that these moduli spaces possess a natural algebraic symplectic structure. We also give an upper bound of the…
We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a…
This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmarked Riemann surfaces, we find there can be many connected…
This paper presents an algebraic-geometric construction of the derivative developed initially within the class of polynomial functions without introducing limits at the initial stage. Tangency is characterized by an algebraic condition: the…
We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
The paper presents an analog of the old result by the author and V. Voevodsky, according to which a Riemann surface admits a conformal structure, defined by an equilateral triangulation, if and only if the corresponding algebraic curve can…
We develop the theory of linear algebra over a (Z_2)^n-commutative algebra (n in N), which includes the well-known super linear algebra as a special case (n=1). Examples of such graded-commutative algebras are the Clifford algebras, in…
Our main theorem classifies the Auslander-Reiten triangles according to properties of the morphisms involved. As a consequence, we are able to compute the mapping cone of an irreducible morphism. We finish by showing a technique for…
In this paper, we build the global determinant method of Salberger by Arakelov geometry explicitly. As an application, we study the dependence on the degree of the number of rational points of bounded height in plane curves. We will also…
Riemann surface carries a natural line bundle, the determinant bundle. The space of sections of this line bundle (or its multiples) constitutes a natural non-abelian generalization of the spaces of theta functions on the Jacobian. There has…
As for any symmetric space the tangent space to Siegel upper-half space is endowed with an operation coming from the Lie bracket on the Lie algebra. We consider the pull-back of this operation to the moduli space of curves via the Torelli…
In this paper, we construct certain rational or integral elements in the motivic cohomology of superelliptic curves which are quotient curves of abelian coverings of $\mathbb{P}^1$ minus $n+2$ points, and prove that these elements are…
We introduce the point degree spectrum of a represented space as a substructure of the Medvedev degrees, which integrates the notion of Turing degrees, enumeration degrees, continuous degrees, and so on. The notion of point degree spectrum…
We develop a coordinate-free probabilistic framework for determinantal point processes associated with Bergman kernels on compact complex manifolds. The basic issue is that Bergman kernels are naturally line-bundle-valued:…
The classic Schneider-Lang theorem in transcendence theory asserts that there are only finitely many points at which algebraically independent complex meromorphic functions of finite order of growth can simultaneously take values in a…
This paper continues the author's previous work on a limit-free algebraic-geometric construction of the derivative in the class of polynomial functions and extends the proposed framework to elementary functions. Derivatives of rational…