Published in Forum Mathematicum
For many classes of models, there are universal members in any cardinal λ which “essentially satisfies GCH, i.e., λ = 2 |T|). But if the class is “complicated enough”, e.g., the class of linear orders, we know that if λ is “regular and not so close to satisfying GCH”, then there is no universal member. Here, we find new sufficient conditions (which...
Published in Forum Mathematicum
We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a more general classification of commutative monoid structures of rank 0, n-1n-1 or 𝑛 on a normal affine variety...
Published in Forum Mathematicum
We apply differential operators to modular forms on orthogonal groups O(2,ℓ){\mathrm{O}(2,\ell)} to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form ϕ are theta l...
Published in Forum Mathematicum
Let Y be a smooth complete intersection of a quadric and a cubic in ℙn{\mathbb{P}^{n}}, with n even. We show that Y has a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, the Chow ring of (powers of) Y displays K3-like behavior. As a by-product of the argument, we also establish a multiplicative Chow–Künneth d...
Published in Forum Mathematicum
This paper aims to introduce a construction technique of set-theoretic solutions of the Yang–Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new solutions. In particular, this method turns out to be useful to provide non-bijective solutions of finite ord...
Published in Forum Mathematicum
We find the number sk(p,Ω)s_{k}(p,\Omega) of cuspidal automorphic representations of GSp(4,AQ)\mathrm{GSp}(4,\mathbb{A}_{\mathbb{Q}}) with trivial central character such that the archimedean component is a holomorphic discrete series representation of weight k≥3k\geq 3, and the non-archimedean component at 𝑝 is an Iwahori-spherical representation...
Published in Forum Mathematicum
We show that, on compact Riemannian surfaces of nonpositive curvature, the generalized periods, i.e. the 𝜈-th order Fourier coefficients of eigenfunctions eλe_{\lambda} over a closed smooth curve 𝛾 which satisfies a natural curvature condition, go to 0 at the rate of O((logλ)-12)O((\log\lambda)^{-\frac{1}{2}}) in the high energy limit λ→∞\lambda\...
Published in Forum Mathematicum
We find the complete integer solutions of the equation X2+Y2+Z2-4XY-4YZ+10XZ=1X^{2}+Y^{2}+Z^{2}-4XY-4YZ+10XZ=1. As an application, we prove that, for each solution (a,b,c)(a,b,c) such that a>0a>0, b-2a>0b-2a>0 and (b-2a)2≥4a(b-2a)^{2}\geq 4a, there is a vector bundle 𝐸 on P3\mathbb{P}^{3} defined by a minimal linear resolution 0→OP3(-2)a→...
Published in Forum Mathematicum
The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth S1{S^{1}}-action vanishes. In the present work, we prove a version of this result for the integral foliated simplicial volume of aspherical manifolds: The integral foliated simplicial volume of aspherical oriented closed connected smooth manifolds th...
Published in Forum Mathematicum
In this paper, we construct a class of new modules for the quantum group Uq(sl2)U_{q}(\mathfrak{sl}_{2}) which are free of rank 1 when restricted to C[K±1]\mathbb{C}[K^{\pm 1}]. The irreducibility of these modules and submodule structure for reducible ones are determined. It is proved that any C[K±1]\mathbb{C}[K^{\pm 1}]-free Uq(sl2)U_{q}(\ma...
