Related papers: Thomae's Derivative Formulae for Trigonal Curves
We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs.
The paper develops the result of second Thomae theorem in hyperelliptic case. The main formula, called general Thomae formula, provides expressions for values at zero of the lowest non-vanishing derivatives of theta functions with singular…
Let $X$ be an Abelian cover $\mathbb{CP}^{1}$ ramified at $mr$ points, $\lambda_1...\lambda_{mr}.$ we define a class of non positive divisors on $X$ of degree $g-1$ supported in the pre images of the branch points on $X$, such that the…
Determinantal formulae for Jacobian theta functions that go back to Klein are elaborated, via an idea due to Matone and Volpato. Also, the natural square roots of theta constants on the moduli space of curves whose existence was shown by…
By analyzing the affine Taylor expansion of a non-degenerate plane curve, we obtain characterizations of classes of such curves via curvature properties of the gravity curve. The proof is based on an analysis of the degree parity and…
In this paper, we prove Thomae's formula for a triple covering of $\bold P^1$ with arbitrary index. This formula gives a relation between theta constants, determinants of period integrals and the difference products of branch points. To…
A complete solution of Mumford's second problem about representation of theta derivatives with rational characteristics in terms of theta constants with rational characteristics is found. An explicit formula for computing such an expression…
The discriminant of a smooth plane cubic curve over the complex numbers can be written as a product of theta functions. This provides an important connection between algebraic and analytic objects. In this paper, we perform a new approach…
Rosenhain's famous formula expresses the periods of first kind integrals of genus two hyperelliptic curves in terms of $\theta$-constants. In this paper we generalize the Rosenhain formula to higher genera hyperelliptic curves by means of…
This paper gives a natural extension of Frobenius-Stickelberger formula and Kiepert formula to Abelian functions for "Purely Trigonal Curves", especially, of degree four. A description on the theory of Abelian functions for general trigonal…
Our aim in this paper is to compute the Poincar\'{e} series of the derivation module of the projective closure of certain affine monomial curves.
In this paper, we develop a geometric approach to study derived tame finite dimensional associative algebras, based on the theory of non-commutative nodal curves.
In this paper we present several formulae for computing the partial degrees of the defining polynomial of the offset curve to an irreducible affine plane curve given implicitly, and we see how these formulae particularize to the case of…
We shall give an elementary and rigorous proof of the Thomae formula for ${\bf Z}_N$ curves which was discovered by Bershadsky and Radul. Instead of using the determinant of the Laplacian we use the traditional variational method which goes…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
We generalize the elementary methods presented in several examples in the book \cite{[FZ]} to obtain the Thomae formulae for general fully ramified $Z_{n}$ curves.
We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function and establish tropical versions of the…
While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…
In this papers, we study the geometric and arithmetic properties of the theta divisor associated to the sheaf of locally exact differential forms over a curve in positive characteristic. In this published version, we prove a stronger…
We show how to calculate the Euler characteristic of an affine Jacobi variety of a spectral curve from its defining equations.