Advances in Mathematics最新文献

英文中文

Vertex algebras related to regular representations of SL2 与SL2正则表示相关的顶点代数

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.aim.2025.110763

Dražen Adamović , Antun Milas

We construct a family of potentially quasi-lisse (non-rational) vertex algebras, denoted by

C_{p}

p \geq 2

, which are closely related to the vertex algebra of chiral differential operators on

S L (2)

at level

- 2 + \frac{1}{p}

. We prove that for

p = 3

, there is an isomorphism between

C_{3}

and the affine vertex algebra

L_{- 5 / 3} (g_{2})

from the Cvitanović-Deligne series. Moreover, we also establish isomorphisms between

C_{4}

and

C_{5}

and certain affine W-algebras of types

F_{4}

and

E_{8}

, respectively. In this way, we resolve the problem of decomposing certain conformal embeddings of affine vertex algebras into affine W-algebras. An important feature is that

C_{p}

\frac{1}{2} Z_{\geq 0}

-graded with finite-dimensional graded subspaces and convergent characters. Therefore, for all

p \geq 2

, we show that the characters of

C_{p}

exhibit modularity, supporting the conjectural quasi-lisse property.

构造了一类潜在的拟无理数顶点代数，记为Cp， p≥2，它们与- 2+1p水平上SL(2)上的手性微分算子的顶点代数密切相关。证明了当p=3时，C3与Cvitanović-Deligne级数中的仿射顶点代数L−5/3（g2）之间存在同构。此外，我们还分别建立了C4和C5与F4和E8型仿射w代数之间的同构关系。这样，我们解决了若干仿射顶点代数的共形嵌入分解为仿射w代数的问题。一个重要的特征是Cp是12Z≥0级的，具有有限维的分级子空间和收敛特征。因此，对于所有p≥2，我们证明了Cp的性质呈现模性，支持了推测的拟lisse性质。

引用次数: 0

Bounded common fundamental domains for two lattices 两个格的有界公共基本域

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.aim.2025.110776

Sigrid Grepstad , Mihail N. Kolountzakis

We prove that for any two lattices

L, M \subseteq R^{d}

of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exists a bounded measurable set

E \subseteq R^{d}

such that E tiles

R^{d}

when translated by L or by M. A consequence of this is that the indicator function of E forms a Weyl–Heisenberg (Gabor) orthogonal basis of

L^{2} (R^{d})

when translated by L and modulated by

M^{⁎}

, the dual lattice of M.

证明了对任意两个体积相同的格L，M≥Rd存在一个可测的、有界的、它们的公共基本域。换句话说，存在一个有界的可测集E≥≥Rd，使得E≥≥Rd时，被L≥≥M时，E的指示函数形成L2（Rd）的weil - heisenberg （Gabor）正交基，≥≥M的对偶格。

引用次数: 0

Isotropic motivic fundamental groups 各向同性动力基群

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.aim.2025.110764

Fabio Tanania

The main goal of this paper is to study relative versions of the category of modules over the isotropic motivic Brown-Peterson spectrum, with a particular emphasis on their cellular subcategories. Using techniques developed by Levine, we equip these categories with motivic t-structures, whose hearts are Tannakian categories over

F_{2}

. This allows to define isotropic motivic fundamental groups, and to interpret relative isotropic Tate motives in the heart as their representations. Moreover, we compute these groups in the cases of the punctured projective line and split tori. Finally, we also apply Spitzweck's derived approach to establish an identification between relative isotropic Tate motives and representations of certain affine derived group schemes, whose 0-truncations coincide with the aforementioned isotropic motivic fundamental groups.

本文的主要目标是研究各向同性动机布朗-彼得森谱上模块类别的相对版本，特别强调它们的细胞子类别。使用Levine开发的技术，我们为这些类别配备动机t结构，其核心是F2上的Tannakian类别。这允许定义各向同性动机基本群，并将心脏中相对各向同性的泰特动机解释为它们的表示。此外，我们还计算了射影线被刺破和环面分裂情况下的这些群。最后，我们还应用Spitzweck的推导方法建立了相对各向同性Tate动机与某些仿射衍生群格式表示之间的识别，这些群的0截断与上述各向同性动机基本群一致。

引用次数: 0

Laurent polynomials and deformations of non-isolated Gorenstein toric singularities 劳伦多项式与非孤立戈伦斯坦环奇点的变形

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.aim.2025.110775

Matej Filip

We establish a correspondence between one-parameter deformations of an affine Gorenstein toric pair

(X_{P}, \partial X_{P})

, defined by a polytope P, and mutations of a Laurent polynomial f with Newton polytope

Δ (f) = P

. For a Laurent polynomial f in two variables, we construct a formal deformation of the three-dimensional Gorenstein toric pair

(X_{Δ (f)}, \partial X_{Δ (f)})

over

C [[T_{f}]]

, where

T_{f}

is the set of deformation parameters arising from mutations. The general fibre of this deformation is smooth if and only if f is 0-mutable. The Kodaira–Spencer map of the constructed deformation is injective, and if f is maximally mutable, then the deformation cannot be nontrivially extended to a larger smooth base space.

我们建立了由多面体P定义的仿射Gorenstein环对（XP,∂XP）的单参数变形与牛顿多面体Δ(f)=P的Laurent多项式f的突变之间的对应关系。对于两个变量的Laurent多项式f，我们构建了三维Gorenstein环对(XΔ（f),∂XΔ(f)） / C[[Tf]]的形式变形，其中Tf是由突变引起的变形参数集。当且仅当f为0可变时，这种变形的一般纤维是光滑的。构造变形的Kodaira-Spencer映射是内射的，如果f是最大可变的，则变形不能非平凡地扩展到更大的光滑基空间。

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引用次数: 0

On Akemann-Weaver conjecture 关于Akemann-Weaver猜想

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.aim.2025.110772

Marcin Bownik

Akemann and Weaver [3] showed Lyapunov-type theorem for rank one positive semidefinite matrices which is an extension of Weaver's KS₂ conjecture [34] that was proven by Marcus, Spielman, and Srivastava [30] in their breakthrough solution of the Kadison-Singer problem [27]. They conjectured that a similar result holds for higher rank matrices. We prove the conjecture of Akemann and Weaver by establishing Lyapunov-type theorem for trace class operators. In the process we prove a matrix discrepancy result for sums of hermitian matrices. This extends rank one result of Kyng, Luh, and Song [28] who established an improved bound in Lyapunov-type theorem of Akemann and Weaver.

Akemann和Weaver[3]给出了秩一正半定矩阵的lyapunov型定理，该定理是Marcus、Spielman和Srivastava[30]在他们对kadson - singer问题[27]的突破性解中证明的Weaver的KS2猜想[34]的推广。他们推测，类似的结果也适用于更高秩的矩阵。通过建立迹类算子的lyapunov型定理，证明了Akemann和Weaver的猜想。在此过程中，我们证明了厄米矩阵和的一个矩阵差异结果。这推广了king， Luh， and Song b[28]在Akemann和Weaver的lyapunov型定理中建立了改进界的第一个结果。

引用次数: 0

Measures that violate the generalized continuum hypothesis 违背广义连续统假设的测度

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.aim.2025.110778

Tom Benhamou , Gabriel Goldberg

A simple

P_{λ}

-point on a regular cardinal κ is a uniform ultrafilter on κ with a mod-bounded decreasing generating sequence of length λ. We prove that if there is a simple

P_{λ}

-point ultrafilter over

κ > ω

, then

λ = d_{κ} = b_{κ} = u_{κ} = r_{κ} = s_{κ}

. We show that such ultrafilters appear in the models of [3], [13]. We improve the lower bound for the consistency strength of the existence of a

P_{κ^{+ +}}

-point to a 2-strong cardinal. Finally, we apply our arguments to obtain non-trivial lower bounds for (1) the statement that the generalized tower number

t_{κ}

is greater than

κ^{+}

and κ is measurable, (2) the preservation of measurability after the generalized Mathias forcing, and (3) variations of filter games of [28], [22], [18] in the case

2^{κ} > κ^{+}

正则基数κ上的一个简单p λ点是一个长度为λ的模有界递减生成序列的κ上的均匀超滤波器。证明了在κ>；ω上存在一个简单的p λ点超滤波器，则λ=dκ=bκ=uκ=rκ=sκ。我们证明了这种超滤体出现在[3]，[13]模型中。我们将Pκ++-点存在一致性强度的下界改进为2强基数。最后，我们应用我们的论证获得了以下条件的非平凡下界：(1)广义塔数tκ大于κ+且κ是可测量的，(2)广义Mathias强迫后可测量性的保存，以及(3)在2κ>；κ+情况下[28]，[22]，[18]的滤波器对策的变化。

引用次数: 0

On the refined analyticity radius of 3-D generalized Navier-Stokes equations 三维广义Navier-Stokes方程的精细解析半径

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.aim.2025.110769

Dong Li , Ping Zhang

<div><div>We analyze the instantaneous growth of analyticity radius for three dimensional generalized Navier-Stokes equations. For the subcritical <math><msup><mrow><mi>H</mi></mrow><mrow><mi>γ</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math> case with <math><mi>γ</mi><mo>></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math>, we prove that there exists a positive time <math><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub></math> so that for any <math><mi>t</mi><mo>∈</mo><mo>]</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>]</mo></math>, the radius of analyticity of the solution u satisfies the pointwise-in-time lower bound<math><mrow><mi>rad</mi></mrow><mo>(</mo><mi>u</mi><mo>)</mo><mo>(</mo><mi>t</mi><mo>)</mo><mo>≥</mo><msqrt><mrow><mo>(</mo><mn>2</mn><mi>γ</mi><mo>−</mo><mn>1</mn><mo>)</mo><mi>t</mi><mo>(</mo><mo>|</mo><mi>ln</mi><mo>⁡</mo><mi>t</mi><mo>|</mo><mo>+</mo><mi>ln</mi><mo>⁡</mo><mo>|</mo><mi>ln</mi><mo>⁡</mo><mi>t</mi><mo>|</mo><mo>+</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></msqrt><mo>,</mo></math> where <math><msub><mrow><mi>K</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>→</mo><mo>∞</mo></math> as <math><mi>t</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></math>. This in particular gives a nontrivial improvement of the previous result by Herbst and Skibsted in [17] for the case <math><mi>γ</mi><mo>∈</mo><mo>]</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>/</mo><mn>2</mn><mo>[</mo></math> and also settles the decade-long open question in [17], namely, whether or not<math><munder><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>inf</mi></mrow></mrow><mrow><mi>t</mi><mo>→</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></munder><mspace></mspace><mfrac><mrow><mrow><mi>rad</mi></mrow><mo>(</mo><mi>u</mi><mo>)</mo><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><msqrt><mrow><mi>t</mi><mo>|</mo><mi>ln</mi><mo>⁡</mo><mi>t</mi><mo>|</mo></mrow></msqrt></mrow></mfrac><mo>≥</mo><msqrt><mrow><mn>2</mn><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msqrt></math> for all <math><mi>γ</mi><mo>≥</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math>. In the critical case <math><msup><mrow><mi>H</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math> we prove that there exists <math><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>></mo><mn>0</mn></math> so that for any <math><mi>t</mi><mo>∈</mo><mo>

本文分析了三维广义Navier-Stokes方程解析半径的瞬时增长。对于含有γ>；12的亚临界Hγ(R3)情形，我们证明了存在一个正时间t0，使得对于任意t∈]0，t0]，解u的可解析性半径满足点向时间下界(u)(t)≥(2γ−1)t(|ln (t) |+ln (|) ln (t) |+Kt)，其中Kt→∞= t→0+。这特别给出了[17]中Herbst和Skibsted对γ∈]1/2,3/2[的非一般改进，并解决了[17]中十年来悬而未决的问题，即对于所有γ≥32，是否liminft→0+rad(u)(t)t|ln (t |)≥2γ−1。在临界情况H12（R3）下证明了存在t1>；0，使得对于任意t∈]0，t1], rad(u)(t)≥λ(t)t且λ(t)满足极限→0+ λ(t)=∞。

引用次数: 0

Motivic cohomology of cyclic coverings 循环覆盖的动机上同调

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.aim.2025.110767

Tariq Syed

Cyclic coverings produce many examples of topologically contractible smooth affine complex varieties. In this paper, we study the motivic cohomology groups of cyclic coverings over algebraically closed fields of characteristic 0. In particular, we prove that in many situations Chow groups of cyclic coverings become trivial after tensoring with

Q

. Furthermore, we can prove that the Chow groups of certain bicyclic coverings are trivial even without tensoring with

Q

循环复盖产生了许多拓扑可收缩光滑仿射复变的例子。研究了特征为0的代数闭域上循环覆盖的动机上同群。特别地，我们证明了在许多情况下，环覆盖的Chow群在与Q张紧后变得平凡，进而证明了某些环覆盖的Chow群即使不与Q张紧也是平凡的。

引用次数: 0

Extremal norms of potentials from fixed eigenvalues or eigenvalues ratio for Camassa-Holm equations Camassa-Holm方程的固定特征值或特征值比值势的极值范数

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.aim.2025.110766

Jifeng Chu , Gang Meng , Zhi Zhang

The aim of this paper is to study a kind of reverse spectral problems for Camassa-Holm equations. We prove the explicit solutions for the extremal

L^{1}

-norms of the potentials, given the first fixed periodic eigenvalue or any fixed Dirichlet eigenvalue, or fixed ratios of Dirichlet eigenvalues. We use the setting of measure differential equations to understand such problems because the solution will lead to Dirac measure distributions of potentials. The explicit expressions for the sharp bounds are given as some elementary functions.

本文的目的是研究一类Camassa-Holm方程的逆谱问题。在给定第一个固定的周期特征值或任意固定的Dirichlet特征值，或Dirichlet特征值的固定比率的情况下，证明了势的极值l1范数的显式解。我们使用测度微分方程的集合来理解这类问题，因为它的解将导致势能的狄拉克测度分布。以一些初等函数的形式给出了尖锐边界的显式表达式。

引用次数: 0

Rationality of singular cubic threefolds over R R上奇异三次三倍的合理性

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2026-01-06 DOI: 10.1016/j.aim.2025.110756

Ivan Cheltsov , Yuri Tschinkel , Zhijia Zhang

We study rationality properties of real singular cubic threefolds.

研究了实奇异三次三重的合理性性质。

引用次数: 0

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