Journal of Geometry and Physics最新文献

英文中文

Maurer–Cartan elements on holomorphic Poisson manifolds 全纯泊松流形上的Maurer-Cartan元

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-12-01 Epub Date: 2025-09-26 DOI: 10.1016/j.geomphys.2025.105665

Youming Chen, Liping Su

In this paper, we consider the Maurer–Cartan equation on holomorphic Poisson manifolds. For a differential graded Lie algebra (DGLA) associated with a holomorphic Poisson structure, we show the existence of its Maurer–Cartan elements under the assumption of the

\partial \bar{\partial}

-lemma or

\partial_{π} \bar{\partial}

-lemma, and discuss their uniqueness under gauge equivalence with certain topological restrictions.

本文研究了全纯泊松流形上的Maurer-Cartan方程。对于与全纯泊松结构相关的微分梯度李代数（DGLA），在∂∂¯-外理或∂π∂¯-外理的假设下，证明了其Maurer-Cartan元的存在性，并讨论了它们在具有一定拓扑限制的规范等价下的唯一性。

引用次数: 0

Connections and Higgs bundles on curves defined over a number field 数域上曲线上的连接和希格斯束

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-12-01 Epub Date: 2025-09-29 DOI: 10.1016/j.geomphys.2025.105664

Indranil Biswas , Sudarshan Gurjar

Let

X_{0}

be an irreducible smooth projective curve defined over

\overline{Q}

and

E

a vector bundle on

X_{0}

. We give a criterion for connections on the base change

E \otimes_{\overline{Q}} C ⟶ X_{0} \times_{Spec \overline{Q}} Spec C

C

to be the base change of some connection on

E

. A similar criterion is given for Higgs fields on

E \otimes_{\overline{Q}} C

设X0是一条定义在Q面上的不可约光滑投影曲线，E是X0上的向量束。我们给出了一个关于E⊗Q - C - X0×SpecQ的连接的基变化的准则E⊗Q - C上的连接是E上的一些连接的基变化的准则。对于E⊗Q - C上的希格斯场也给出了类似的准则

引用次数: 0

Gap-p Virasoro Lie conformal algebra and extensions of modules Gap-p Virasoro Lie共形代数与模的扩展

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-12-01 Epub Date: 2025-10-22 DOI: 10.1016/j.geomphys.2025.105685

Xiaojian Shi, Xiaoqing Yue

The gap-p Virasoro algebra, which is closely related to the Heisenberg-Virasoro algebra and the algebra of derivations over a quantum torus, plays an important role in both mathematics and mathematical physics. In this paper, we first construct the gap-p Virasoro Lie conformal algebra

{HV}^{p}

from gap-p Virasoro algebra. Then we concretely determine the conformal derivations and conformal biderivations of this Lie conformal algebra. Furthermore, we investigate finite irreducible conformal modules and characterize nontrivial central extensions of

{HV}^{p}

. Based on these results, we finally give a complete classification of extensions of finite irreducible conformal modules over gap-p Virasoro Lie conformal algebra

{HV}^{p}

gap- Virasoro代数与海森堡-Virasoro代数和量子环面上的推导代数密切相关，在数学和数学物理中都占有重要地位。本文首先从gap- Virasoro代数构造gap- Virasoro Lie共形代数HVp。然后具体确定了该李共形代数的共形导数和共形双导数。进一步，我们研究了有限不可约共形模，并刻画了HVp的非平凡中心扩展。基于这些结果，我们最后给出了gap-p Virasoro - Lie共形代数HVp上有限不可约共形模的扩展的完全分类。

引用次数: 0

Manin triples, bialgebras and Yang-Baxter equation of A3-associative algebras 3-结合代数的Manin三元组、双代数和Yang-Baxter方程

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-12-01 Epub Date: 2025-10-22 DOI: 10.1016/j.geomphys.2025.105686

Yaxi Jiang, Chuangchuang Kang, Jiafeng Lü

A_{3}

-associative algebra is a generalization of associative algebra and is one of the four remarkable types of Lie-admissible algebras, along with associative algebra, left-symmetric algebra and right-symmetric algebra. This paper develops bialgebra theory for

A_{3}

-associative algebras. We introduce Manin triples and bialgebras for

A_{3}

-associative algebras, prove their equivalence using matched pairs of

A_{3}

-associative algebras, and define the

A_{3}

-associative Yang-Baxter equation and triangular

A_{3}

-associative bialgebras. Additionally, we introduce relative Rota-Baxter operators to provide skew-symmetric solutions of the

A_{3}

-associative Yang-Baxter equation.

a3 -关联代数是对关联代数的推广，是与关联代数、左对称代数、右对称代数并列的四种显著的李可容许代数类型之一。本文发展了a3 -结合代数的双代数理论。引入了a3结合代数的Manin三元组和双代数，利用a3结合代数的配对对证明了它们的等价性，并定义了a3结合Yang-Baxter方程和三角形a3结合双代数。此外，我们引入相对Rota-Baxter算子，给出a3 -关联Yang-Baxter方程的偏对称解。

引用次数: 0

Noninvertible symmetries in the B model TFT B模型TFT中的不可逆对称性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-12-01 Epub Date: 2025-09-23 DOI: 10.1016/j.geomphys.2025.105653

Andrei Căldăraru , Tony Pantev , Eric Sharpe , Benjamin Sung , Xingyang Yu

In this paper we explore noninvertible symmetries in general (not necessarily rational) SCFTs and their topological B-twists for Calabi-Yau manifolds. We begin with a detailed overview of defects in the topological B model. For trivial reasons, all defects in the topological B model are topological operators, and define (often noninvertible) symmetries of that topological field theory, but only a subset remain topological in the physical (i.e., untwisted) theory. For a generic target space Calabi-Yau X, we discuss geometric realizations of those defects, as simultaneously A- and B-twistable complex Lagrangian and complex coisotropic branes on

X \times X

, and discuss their fusion products. To be clear, the possible noninvertible symmetries in the B model are more general than can be described with fusion categories. That said, we do describe realizations of some Tambara-Yamagami categories in the B model for an elliptic curve target, and also argue that elliptic curves can not admit Fibonacci or Haagerup structures. We also discuss how decomposition is realized in this language.

本文研究了Calabi-Yau流形的一般（不一定是有理的）scft及其拓扑b -扭转的不可逆对称性。我们从拓扑B模型中缺陷的详细概述开始。由于一些微不足道的原因，拓扑B模型中的所有缺陷都是拓扑算子，并且定义了该拓扑场理论的对称性（通常是不可逆的），但在物理（即未扭曲）理论中只有一个子集保持拓扑性。对于一般目标空间Calabi-Yau X，我们讨论了这些缺陷在X×X上同时作为a -和b -可扭转复拉格朗日膜和复共同性膜的几何实现，并讨论了它们的融合产物。需要明确的是，B模型中可能存在的不可逆对称性比用融合范畴所能描述的更为普遍。也就是说，我们确实描述了椭圆曲线目标的B模型中一些Tambara-Yamagami类别的实现，并且还认为椭圆曲线不能承认斐波那契或哈格鲁普结构。我们还讨论了如何在这种语言中实现分解。

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引用次数: 0

Eguchi-Hanson harmonic spinors revisited 重新审视了Eguchi-Hanson谐波旋量

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-11-01 Epub Date: 2025-09-03 DOI: 10.1016/j.geomphys.2025.105640

Guido Franchetti , Kirill Krasnov

We revisit the problem of determining the zero modes of the Dirac operator on the Eguchi-Hanson space. It is well known that there are no normalisable zero modes, but such zero modes do appear when the Dirac operator is twisted by a

U (1)

connection with

L^{2}

normalisable curvature. The main novelty of our treatment is that we use the established formalism of spin-c spinors as complex differential forms, which makes the required calculations remarkably straightforward. In particular, to compute the Dirac operator we never need to compute the spin connection. As a result, we are able to reproduce the known normalisable zero modes of the twisted Eguchi-Hanson Dirac operator by relatively simple computations. We also collect various different descriptions of the Eguchi-Hanson space, including its construction as a hyperkähler quotient of

C^{4}

with the flat metric. The latter illustrates the geometric origin of the connection with

L^{2}

curvature used to twist the Dirac operator. To illustrate the power of the formalism developed, we generalise the results to the case of Dirac zero modes on the Ricci-flat Kähler manifolds obtained by applying Calabi's construction to the canonical bundle of

C P^{n}

我们重新讨论了Eguchi-Hanson空间上Dirac算子零模的确定问题。众所周知，没有可归一化的零模，但当Dirac算子被具有L2可归一化曲率的U(1)连接扭曲时，确实会出现这样的零模。我们的处理的主要新颖之处在于，我们使用已建立的自旋-c旋量的形式作为复杂的微分形式，这使得所需的计算非常简单。特别地，为了计算狄拉克算子，我们不需要计算自旋连接。结果，我们能够通过相对简单的计算再现扭曲Eguchi-Hanson Dirac算子的已知可归一化零模。我们还收集了Eguchi-Hanson空间的各种不同描述，包括其作为C4与平面度量的hyperkähler商的构造。后者说明了用于扭曲狄拉克算子的L2曲率连接的几何起源。为了说明所开发的形式主义的力量，我们将结果推广到ricci平面Kähler流形上的Dirac零模的情况，该结果是通过将Calabi构造应用于CPn的正则束而得到的。

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引用次数: 0

Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume 负体积双曲肖特基流形填充黎曼曲面

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-11-01 Epub Date: 2025-08-21 DOI: 10.1016/j.geomphys.2025.105628

Tommaso Cremaschi , Viola Giovannini , Jean-Marc Schlenker

We provide conditions under which a Riemann surface X is the asymptotic boundary of a convex co-compact hyperbolic manifold, homeomorphic to a handlebody, of negative renormalized volume. We prove that this is the case when there are on X enough closed curves of short enough hyperbolic length.

给出了黎曼曲面X是负重正化体积同胚的凸协紧双曲流形的渐近边界的条件。当X上有足够短的双曲长度的闭曲线时，我们证明了这一点。

引用次数: 0

Deformations of calibrated subbundles in noncompact manifolds of special holonomy via twisting by special sections 特殊完整非紧流形中经特殊截面扭转的标定子束变形

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-11-01 Epub Date: 2025-08-26 DOI: 10.1016/j.geomphys.2025.105631

Romy Marie Merkel

We study special Lagrangian submanifolds in the Calabi–Yau manifold

T^{⁎} S^{n}

with the Stenzel metric, as well as calibrated submanifolds in the

G_{2}

-manifold

Λ_{-}^{2} (T^{⁎} X)

(X^{4} = S^{4}, {CP}^{2})

and the

Spin (7)

-manifold

, both equipped with the Bryant–Salamon metrics. We twist naturally defined calibrated subbundles by sections of the complementary bundles and derive conditions for the deformations to be calibrated. We find that twisting the conormal bundle

N^{⁎} L

L^{q} \subset S^{n}

by a 1-form

μ \in Ω^{1} (L)

does not provide any new examples because the Lagrangian condition requires μ to vanish. Furthermore, we prove that the twisted bundles in the

G_{2}

- and

Spin (7)

-manifolds are associative (coassociative) and Cayley, respectively, if the base is minimal (negative superminimal) and the section holomorphic (parallel). This demonstrates that the (co-)associative and Cayley subbundles allow deformations destroying the linear structure of the fiber, while the base space remains of the same type after twisting. While the results for the two spaces of exceptional holonomy are in line with the findings in Euclidean spaces established by Karigiannis and Leung (2012), the special Lagrangian bundle construction in

T^{⁎} S^{n}

is much more rigid than in the case of

T^{⁎} R^{n}

我们研究了具有Stenzel度量的Calabi-Yau流形T Sn中的特殊拉格朗日子流形，以及具有Bryant-Salamon度量的g2流形Λ−2(T X) （X4=S4,CP2）和Spin(7)-流形中的校准子流形。我们通过互补束的部分扭曲自然定义的校准子束，并推导出要校准的变形的条件。我们发现，将Lq∧Sn的法向束N L以1-形式μ∈Ω1(L)扭转并不能提供任何新的例子，因为拉格朗日条件要求μ消失。进一步证明了在基极小（负超极小）和截面全纯（平行）的情况下，G2-和Spin(7)-流形中的扭束分别是结合的（协协的）和Cayley的。这表明（共）缔合和Cayley亚束允许变形破坏纤维的线性结构，而基底空间在扭转后仍保持相同类型。虽然这两个特殊完整空间的结果与Karigiannis和Leung（2012）在欧几里得空间中的发现一致，但T Sn中的特殊拉格朗日束构造比T Rn中的刚性要大得多。

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引用次数: 0

Surfaces of three-dimensional homogeneous plane waves 三维均匀平面波的表面

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-11-01 Epub Date: 2025-07-25 DOI: 10.1016/j.geomphys.2025.105603

Giovanni Calvaruso, Lorenzo Pellegrino

We investigate the geometry of surfaces in three-dimensional homogeneous non-symmetric plane waves. In particular, we obtain the full classification and explicit description of their totally geodesic and parallel examples and prove the nonexistence of proper totally umbilical surfaces. Moreover, we characterize their minimal surfaces, providing some explicit examples.

研究了三维均匀非对称平面波中表面的几何形状。特别地，我们得到了它们的完全测地线和平行例子的完全分类和显式描述，并证明了适当的完全脐带曲面的不存在性。此外，我们描述了它们的最小曲面，并提供了一些明确的例子。

引用次数: 0

Concave symplectic toric fillings 凹辛环填充

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics

Pub Date : 2025-11-01 Epub Date: 2025-08-08 DOI: 10.1016/j.geomphys.2025.105622

Aleksandra Marinković

As shown by Etnyre and Honda ([2]), every contact 3-manifold admits infinitely many concave symplectic fillings that are mutually not symplectomorphic and not related by blow ups. In this note we refine this result in the toric setting by showing that every contact toric 3-manifold admits infinitely many concave symplectic toric fillings that are mutually not equivariantly symplectomorphic and not related by blow ups. The concave symplectic toric structure is constructed on certain linear and cyclic plumbings over spheres.

如Etnyre和Honda（[2]）所示，每一个接触3流形都允许无限多个凹形辛填充，这些凹形辛填充相互之间不是辛形态的，并且与膨胀无关。在这篇笔记中，我们通过证明每一个接触环形3-流形都允许无限多个凹辛环填充，这些填充相互不等辛且不与膨胀相关。在球面上的一定线性循环管道上构造凹辛环结构。

引用次数: 0

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Journal of Geometry and Physics

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