Mathematische Zeitschrift最新文献

Let ({mathcal {X}}rightarrow C) be a flat k-morphism between smooth integral varieties over a finitely generated field k such that the generic fiber X is smooth, projective and geometrically connected. Assuming that C is a curve with function field K, we build a relation between the Tate-Shafarevich group of (textrm{Pic}^0_{X/K}) and the geometric Brauer groups of ({mathcal {X}}) and X, generalizing a theorem of Artin and Grothendieck for fibered surfaces to higher relative dimensions.

Intermediate dimensions were recently introduced by Falconer et al. (Math Z 296:813–830, 2020) to interpolate between the Hausdorff and box-counting dimensions. In this paper, we show that for every subset E of the symbolic space, the intermediate dimensions of the projections of E under typical self-affine coding maps are constant and given by formulas in terms of capacities. Moreover, we extend the results to the generalized intermediate dimensions introduced by Banaji (Monatsh Math 202: 465–506, 2023) in several settings, including the orthogonal projections in Euclidean spaces and the images of fractional Brownian motions.

Given an NQC log canonical generalized pair ((X,B+M)) whose underlying variety X is not necessarily (mathbb {Q})-factorial, we show that one may run a ((K_X+B+M))-MMP with scaling of an ample divisor which terminates, provided that ((X,B+M)) has a minimal model in a weaker sense or that (K_X+B+M) is not pseudo-effective. We also prove the existence of minimal models of pseudo-effective NQC log canonical generalized pairs under various additional assumptions, for instance when the boundary contains an ample divisor.

In this paper we study the following problem: for a given bounded positive function f on a filtered probability space can we find another function (a multiplier) m, (0le mle 1), such that the function mf is not “too small” but its square function is bounded? We explicitly show how to construct such multipliers for the usual martingale square function and for so-called conditional square function. Besides that, we show that for the usual square function more general statement can be obtained by application of a non-constructive abstract correction theorem by Kislyakov.

Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that (H^j(X,Omega ^i_Xotimes L)=0) for (j>0), (ige 0), and L ample. This holds for toric varieties, but not for most other varieties. We classify the smooth Fano threefolds that satisfy Bott vanishing. There are many more than expected.

We prove existence and regularity of metrics which minimize combinations of Steklov eigenvalues over metrics of unit perimeter on a surface with boundary. We show that there are free boundary minimal immersions into ellipsoids parametrized by eigenvalues, such that the coordinate functions are eigenfunctions with respect to the minimal metrics. This work generalizes Fraser–Schoen’s and the author’s maximization for one eigenvalue among metrics of unit perimeter on a surface giving free boundary minimal immersions into balls. We also generalize the previous results of critical metrics for one eigenvalue to any combination of eigenvalues from target balls to target ellipsoids.

Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the derived category D(Mod-R). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with methods from the model theory of modules and Auslander-Reiten theory.

We unfold the theta integrals defining the Kudla–Millson lift of genus 1 associated to even lattices of signature (b, 2), where (b>2). This enables us to compute the Fourier expansion of such defining integrals and prove the injectivity of the Kudla–Millson lift. Although the latter result has been already proved in [5], our new procedure has the advantage of paving the ground for a strategy to prove the injectivity of the lift also for the cases of general signature and of genus greater than 1.

We study the reflections of locally free Caldero–Chapoton functions associated to representations of Geiß–Leclerc–Schröer’s quivers with relations for symmetrizable Cartan matrices. We prove that for rank 2 cluster algebras, non-initial cluster variables are expressed as locally free Caldero–Chapoton functions of locally free indecomposable rigid representations. Our method gives rise to a new proof of the locally free Caldero–Chapoton formulas obtained by Geiß–Leclerc–Schröer in Dynkin cases. For general acyclic skew-symmetrizable cluster algebras, we prove the formula for any non-initial cluster variable obtained by almost sink and source mutations.

In this paper, we build a compactification by a strictly pseudoconvex CR structure for a complete and non-compact Kähler manifold whose curvature tensor is asymptotic to that of the complex hyperbolic space. To do so, we study in depth the evolution of various geometric objects that are defined on the leaves of some foliation of the complement of a suitable convex subset, called an essential subset, whose leaves are the equidistant hypersurfaces above this latter subset. With a suitable renormalization which is closely related to the anisotropic nature of the ambient geometry, the above mentioned geometric objects converge near infinity, inducing the claimed structure on the boundary at infinity.