Mathematische Zeitschrift最新文献

We explore the relationship between fibrations arising naturally from a surjective morphism to an abelian variety. These fibrations encode geometric information about the morphism. Our study focuses on the interplay of these fibrations and presents several applications. Then we propose a generalization of the Iitaka conjecture which predicts an equality of Kodaira dimension of fibrations, and prove it when the base is a smooth projective variety of maximal Albanese dimension.

Let F be an algebraically closed field of positive characteristic and let R be a finitely generated F-algebra with a filtration with the property that the associated graded ring of R is a finitely generated integral domain of Krull dimension two. We show that under these conditions R satisfies a polynomial identity, answering a question of Etingof in the affirmative in a special case.

This article is the continuation of the work [30] where we had proved maximal estimates

for sectorial operators A acting on (L^p(Omega ,Y)) (Y being a UMD lattice) and admitting a Hörmander functional calculus (a strengthening of the holomorphic (H^infty ) calculus to symbols m differentiable on ((0,infty )) in a quantified manner), and (m : (0, infty ) rightarrow mathbb {C}) being a Hörmander class symbol with certain decay at (infty ). In the present article, we show that under the same conditions as above, the scalar function (t mapsto m(tA)f(x,omega )) is of finite q-variation with (q > 2), a.e. ((x,omega )). This extends recent works by [13, 44,45,46, 52, 61] who have considered among others (m(tA) = e^{-tA}) the semigroup generated by (-A). As a consequence, we extend estimates for spherical means in euclidean space from [52] to the case of UMD lattice-valued spaces. A second main result yields a maximal estimate

for the same A and similar conditions on m as above but with (f_t) depending itself on t such that (t mapsto f_t(x,omega )) belongs to a Sobolev space (Lambda ^beta ) over ((mathbb {R}_+, frac{dt}{t})). We apply this to show a maximal estimate of the Schrödinger (case (A = -Delta )) or wave (case (A = sqrt{-Delta })) solution propagator (t mapsto exp (itA)f). Then we deduce from it solutions to variants of Carleson’s problem of pointwise convergence [18]

for A a Fourier multiplier operator or a differential operator on an open domain (Omega subseteq mathbb {R}^d) with boundary conditions.

We study the rationality of the Peskine sixfolds in ({textbf{P}}^9). We prove the rationality of the Peskine sixfolds in the divisor ({mathcal {D}}^{3,3,10}) inside the moduli space of Peskine sixfolds and we provide a cohomological condition which ensures the rationality of the Peskine sixfolds in the divisor ({mathcal {D}}^{1,6,10}) [(notation from Benedetti and Song (Divisors in the moduli space of Debarre-Voisin varieties, http://arxiv.org/abs/2106.06859, 2021)]. We conjecture, as in the case of cubic fourfolds containing a plane, that the cohomological condition translates into a cohomological and geometric condition involving the Debarre-Voisin hyperkähler fourfold associated to the Peskine sixfold.

In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained inequalities include Hardy, Sobolev, Rellich, Hardy–Littllewood–Sobolev, Gagliardo–Nirenberg, Caffarelli–Kohn–Nirenberg and Heisenberg–Pauli–Weyl type uncertainty inequalities. Some of these estimates have been known in the case of the sub-Laplacians, however, for more general hypoelliptic operators almost all of them appear to be new as no approaches for obtaining such estimates have been available. The approach developed in this paper relies on establishing integral versions of Hardy inequalities on homogeneous Lie groups, for which we also find necessary and sufficient conditions for the weights for such inequalities to be true. Consequently, we link such integral Hardy inequalities to different hypoelliptic inequalities by using the Riesz and Bessel kernels associated to the described hypoelliptic operators.

Let G be (S_{mathbb {N}}), the finitary permutation (i.e., permutations with finite support) group on the set of positive integers (mathbb {N}). We prove that G has the invariant von Neumann subalgebras rigidity (ISR, for short) property as introduced in Amrutam–Jiang’s work. More precisely, every G-invariant von Neumann subalgebra (Psubseteq L(G)) is of the form L(H) for some normal subgroup (Hlhd G) and in this case, (H={e}, A_{mathbb {N}}) or G, where (A_{mathbb {N}}) denotes the finitary alternating group on (mathbb {N}), i.e., the subgroup of all even permutations in (S_{mathbb {N}}). This gives the first known example of an infinite amenable group with the ISR property.

The paper provides a detailed study of crucial inequalities for smoothness and interpolation characteristics in rearrangement invariant Banach function spaces. We present a unified approach based on Holmstedt formulas to obtain these estimates. As examples, we derive new inequalities for moduli of smoothness and K-functionals in various Lorentz spaces.

We reformulate the twisted 1-loop invariant in terms of Ptolemy coordinates. In addition, we prove that the twisted 1-loop invariant is equal to the adjoint twisted Alexander polynomial for all hyperbolic once-punctured torus bundles. This shows that the 1-loop conjecture proposed by Dimofte and Garoufalidis holds for all hyperbolic once-punctured torus bundles.

We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids. We also establish invariance of the dynamic asymptotic dimension under Morita equivalence. In the second part of the article, we consider a canonical coarse structure on an étale groupoid, and compare the asymptotic dimension of the resulting coarse space with the dynamic asymptotic dimension of the underlying groupoid.

In this article, we consider the set of points for the holding of the equality in a weighted version of Suita conjecture for higher derivatives, and give relations between the set and the integer valued points of a class of harmonic functions (maybe multi-valued). For planar domains bounded by finite analytic closed curves, we give relations between the set and Dirichlet problem.