相关论文: A product formula for volumes of varieties

We introduce a generalization of the product expansion of a finite semigroup. As an application, we provide an alternative proof of the decidability of pointlike sets for pseudovarieties consisting of semigroups whose subgroups all belong…

We prove a product formula for $\delta$-invariant and as an application, we show that product of K-(semi, poly)stable Fano varieties is also K-(semi, poly)stable.

We represent the volume product for the unit p-ball in a a form free of its gamma symbolism;this will enable us to confirm Mahler's lower bound and Santalo's upper bound by the use of basic only gamma function theory and moderately advanced…

We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.

This short note delivers, via elementary calculations, a product representation of pi.

We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidirect products of groups.

This is an expository note on useful expressions for the density function of a product of independent random variables where each variable has a Beta distribution.

We generalize the author's formula for Gromov-Witten invariants of symplectic toric manifolds (see math.AG/0006156) to those needed to compute the quantum product of more than two classes directly, i.e. involving the pull-back of the…

We establish a product formula for Gromov-Witten invariants for closed, connected, relatively semi-positive Hamiltonian fibrations over any symplectic base. Furthermore, we show that the fibration projection induces a locally trivial…

The Mal'tsev product of two varieties of similar algebras is always a quasivariety. We consider the question of when this quasivariety is a variety. The main result asserts that if $\mathcal{V}$ is a strongly irregular variety with no…

We construct the quasi-classical approximation of the form factors in finite volume using the separation of variables. The latter is closely related to the Baxter equation.

Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear…

We study the relationship between the tensor product multiplicities of a compact semisimple Lie algebra $\mathfrak{g}$ and a special function $\mathcal{J}$ associated to $\mathfrak{g}$, called the volume function. The volume function arises…

The convolution product of two conjugacy classes of the unitary group $U_n$ is described by a probability distribution on the space of central measures. Relating this convolution to the quantum cohomology of Grassmannians and using recent…

In 2014, Ibrahim M Alabdulmohsin wrote a paper called "Summability Calculus" where he developed a method to generalize sigma notation to non-integer upper bounds. His paper included a theorem, known as Theorem 6.1.1 (denoted here as Lemma…

The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the…

We introduce the volume function for hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence,…

The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano-Regge type of asymptotic of…

The notion of a generalized product, refining that of a (symmetric and smooth) simplicial space is introduced and shown to imply the existence of an algebra of pseudodifferential operators. This encompasses many constructions of such…

We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a…