Related papers: Rational Products of Singular Moduli

We treat two different equations involving powers of singular moduli. On the one hand, we show that, with two possible (explicitly specified) exceptions, two distinct singular moduli j(\tau),j(\tau') such that the numbers 1, j(\tau)^m and…

We show that all triples $(x_1,x_2,x_3)$ of singular moduli satisfying $x_1 x_2 x_3 \in \mathbb{Q}^{\times}$ are "trivial". That is, either $x_1, x_2, x_3 \in \mathbb{Q}$; some $x_i \in \mathbb{Q}$ and the remaining $x_j, x_k$ are distinct,…

Let $X$ be a nonsingular rational variety. We prove that $X\times \mathbb{C}^2$ is uniformly rational. It follows that nonsingular stably rational varieties are stably uniformly rational.

We study rationality properties of real singular cubic threefolds.

The regularized product of the Fibonacci numbers is evaluated.

We compute the product of any $n$-tuple of conjugacy classes in $SL_2(R)$

We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.

In this paper, we study the formulae for a product of two product Euler polynomials. From this study, we derive some formulae for the integral of the product of two or more Ruler polynomials.

A study of products of factorials modulo p and complete residues.

In this, largely expository, note, we show how the simplicial structure of the moduli spaces of stable rational curves with marked points allows to produce explicit equations for these spaces. The key argument is an elementary combinatorial…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

Rational pairs generalize the notion of rational singularities to reduced pairs $(X,D)$. In this paper we deal with the problem of determining whether a normal variety $X$ has a rationalizing divisor, i.e. a reduced divisor $D$ such that…

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…

We apply Zagier's result for the traces of singular moduli to construct Borcherds products in higher level cases.

Given a singular modulus $j_0$ and a set of rational primes $S$, we study the problem of effectively determining the set of singular moduli $j$ such that $j-j_0$ is an $S$-unit. For every $j_0 \neq 0$, we provide an effective way of finding…

In this article we consider rational functions on algebraic curves, which have one zero and one pole (and call pair of such function and curve Abel pair). We investigate moduli spaces of such functions on curves of genus one; the number of…

We prove rationality results for moduli spaces of elliptic K3 surfaces and elliptic rational surfaces with fixed monodromy groups.

Given a properly normalized parametrization of a genus-0 modular curve, the complex multiplication points map to algebraic numbers called singular moduli. In the classical case, the maps can be given analytically. However, in the Shimura…

This paper studies the moduli space of stable surfaces of general type. The moduli space component containing the moduli point of a product of smooth curves of general type is proved to be the product of the moduli spaces of the curves,…

In this paper we introduce a notion of rational singularities associated to pairs $(X, \ba^t)$ where $X$ is a variety, $\ba$ is an ideal sheaf and $t$ is a nonnegative real number. We prove that most standard results about rational…