首页/论文/2008.09366

arXiv 2008.093662020-08-21math.AGmath.CV

Note on Lisbon integrals and their associated D--modules

Daniel Barlet

英文摘要：

The aim of this Note is to specify the links between the three kinds of Lisbon integrals, trace functions and trace forms with the corresponding D--modules.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

On Lisbon integrals

We introduce new complex analytic integral transforms, the Lisbon Integrals, which naturally arise in the study of the affine space $\mathbb{C}^k$ of unitary polynomials $P_s(z)$ where $s\in\mathbb{C}^k$ and $z\in \mathbb{C}$, $s_i$ identified to the $i-$th symmetric function of the roots of $P_s(z)$. We completely determine the $\mathcal{D}$-modules (or systems of partial differential equations) the Lisbon Integrals satisfy and prove that they are their unique global solutions. If we specify a holomorphic function $f$ in the $z$-variable, our construction induces an integral transform which a…

2020-02-23math.AGmath.CV

A note on some fiber-integrals

We remark that the study of a fiber-integral of the type F (s) := f =s ($ω$/df) $\land$ ($ω$/df) either in the local case where $ρ$ $\not\equiv$ 1 around 0 is C $\infty$ and compactly supported near the origin which is a singular point of {f = 0} in C n+1 , or in a global setting where f : X $\rightarrow$ D is a proper holomorphic function on a complex manifold X, smooth outside {f = 0} with $ρ$ $\not\equiv$ 1 near {f = 0}, for given holomorphic (n+1)--forms $ω$ and $ω$' , that a better control on the asymptotic expansion of F when s $\rightarrow$ 0, is obtained by using the Bernstein polynomi…

2015-12-22math.AGmath.CV

Note on the counterexamples for the integral Tate conjecture over finite fields

In this note we discuss some examples of non torsion and non algebraic cohomology classes for varieties over finite fields. The approach follows the construction of Atiyah-Hirzebruch and Totaro.

2014-01-08math.AG

A note on a question of Shioda about integral sections

We consider a rational elliptic surface with a relatively minimal fibration. We compute the number of integral sections in the above rational elliptic surface. As an application, we obtain an estimate of polynomial solutions of some equations.

2024-01-01math.AG

A Note on Twistor Integrals

An exposition of the basic geometry of twistor integrals, intended for mathematicians.

2013-02-14math-phmath.AGmath.MP

Notes on the A_inf-cohomology of Integral p-adic Hodge theory

We present a detailed overview of the construction of the A_inf-cohomology theory from the preprint "Integral p-adic Hodge theory", joint with B. Bhatt and P. Scholze. We focus particularly on the p-adic analogue of the Cartier isomorphism via relative de Rham--Witt complexes.

2016-08-02math.AGmath.NT

更多相关论文收起更多论文

关于 Wirtinger 积分的扭结同调与上同调群的注记

Notes on twisted homology and cohomology groups for the Wirtinger integral

Otaru University of Commerce（小樽商科大学）；Kitami Institute of Technology（北见工业大学）

本文研究 Wirtinger 积分相关的扭结同调与上同调群的结构，利用复环面上的对合将其分解为关于相交形式正交的特征空间，并证明相应的相交矩阵具有简单形式。

2026-05-25math.AGmath.CA

A note on critical points of integrals of soliton equations

We consider the problem of extending the integrals of motion of soliton equations to the space of all finite-gap solutions. We consider the critical points of these integrals on the moduli space of Riemann surfaces with marked points and jets of local coordinates. We show that the solutions of the corresponding variational problem have an explicit description in terms of real-normalized differentials on the spectral curve. Such conditions have previously appeared in a number of problems of mathematical physics.

2010-05-20math-phmath.AGmath.MP

A note on periods of Calabi--Yau fractional complete intersections

We prove that the GKZ $\mathscr{D}$-module $\mathcal{M}_{A}^β$ arising from Calabi--Yau fractional complete intersections in toric varieties is complete, i.e., all the solutions to $\mathcal{M}_{A}^β$ are period integrals. This particularly implies that $\mathcal{M}_{A}^β$ is equivalent to the Picard--Fuchs system. As an application, we give explicit formulae of the period integrals of Calabi--Yau threefolds coming from double covers of $\mathbf{P}^{3}$ branch over eight hyperplanes in general position.

2022-04-22math.AG

关于二维 $\mathbb F_p$-Selberg 积分的注记

Notes on $2D$ $\mathbb F_p$-Selberg integrals

本研究证明了依赖于多组正整数参数、取值于奇素数阶有限域的二维 $\mathbb F_p$-Selberg 积分公式，其灵感源于KZ方程的多维超几何解与模p约化后多项式解的相似性，丰富了有限域上积分公式的研究成果。

2024-09-13math-phmath.AGmath.MP

A note on abelian arithmetic BF-theory

We compute some arithmetic path integrals for BF-theory over the ring of integers of a totally imaginary field, which evaluate to natural arithmetic invariants associated to $\mathbb{G}_m$ and abelian varieties.

2019-11-06math-phmath.AGmath.AT