Related papers: Rational Products of Singular Moduli

We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete…

We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.

We prove that good quotients of algebraic varieties with 1-rational singularities also have 1-rational singularities. This refines a result of Boutot on rational singularities of good quotients.

We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.

We present two methods for computing the rational singular locus of the closure of a nilpotent orbit in a complex semisimple Lie algebra and give a number of interesting examples.

Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.

We prove that the moduli spaces of framed bundles over a smooth projective curve are rational. We compute the Brauer group of these moduli spaces to be zero under some assumption on the stability parameter.

We prove a refinement of the results of Gross and Zagier on prime factorizations of singular moduli.

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

We classify pairs of conjugacy classes in almost simple algebraic groups whose product consists of finitely many classes. This leads to several interesting families of examples which are related to a generalization of the Baer--Suzuki…

We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that…

We prove that singularities with holomorphic monodromies are preserved by the Hadamard product. We find an explicit formula for the monodromy of the singularities, and similar formulas for the exponential e\~ne product. Using these formulas…

The moduli spaces of trigonal curves are proven to be rational when the genus is divisible by 4.

We characterize pairs of rational functions $A$, $B$ such that $A$ is semiconjugate to $B$, and $B$ is semiconjugate to $A$.

Let $g$ be a principal modulus with rational Fourier coefficients for a discrete subgroup of $\mathrm{SL}_2(\mathbb{R})$ between $\Gamma(N)$ or $\Gamma_0(N)^\dag$ for a positive integer $N$. Let $K$ be an imaginary quadratic field. We give…

We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli…

Building on the classification of modules for algebraic groups with finitely many orbits on subspaces, we determine all faithful irreducible modules for simple and maximal-semisimple connected algebraic groups that are orthogonal and have…

Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial. In this…

We describe several infinite series of rational conformal field theories whose conformal characters are modular units, i.e. which are modular functions having no zeros or poles in the upper complex half plane, and which thus possess simple…

In this note, we give a new simple system of global parameters on the moduli space of rational functions, and clarify the relation to the parameters indicating location of fixed points and the indices at them. As a byproduct, we solve a…