Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 0704.2744

Nahm transform and parabolic minimal Laplace transform

Szilard Szabo
View original source ↗Read source document ↗Export metadata ↓

Abstract

We prove that Nahm transform for integrable connections with a finite number of regular singularities and an irregular singularity of rank 1 on the Riemann sphere is equivalent -- up to considering integrable connections as holonomic $\D$-modules -- to minimal Laplace transform. We assume semi-simplicity and resonance-freeness conditions, and we work in the framework of objects with a parabolic structure. In particular, we describe the definition of the parabolic version of Laplace transform due to C. Sabbah. The proof of the main result relies on the study of a twisted de Rham complex.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Szilard Szabo. 2011-09-02. Nahm transform and parabolic minimal Laplace transform. https://arxiv.org/abs/0704.2744

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Containment problems for fat point schemes via asymptotic multiplier ideals

We study a multiplier-ideal approach to the containment problem for radical ideals of points in projective space. The expected asymptotic multiplier-ideal computation depends on controlling residual base loci of the relevant symbolic linear systems. We isolate this issue in the notion of clean asymptotic multiplier ideals. Under this hypothesis, a failure of \[ I^{(2r-1)}\not\subseteq I^r \] forces \[ 2r\widehatα(I)\geq α(I^{(2r-1)})+3, \] and in particular $\widehatα(I)\geq 3$. We show that the dual-Hesse configuration is clean although its symbolic systems have a genuinely non-trivial residual asymptotic base part. We also verify cleanliness for star configurations of lines, giving a further infinite family of non-monomial examples, and formulate a cleanliness conjecture for singular loci of line arrangements.

math.AG↗
arXiv2026

An algebraic proof of Hrushovski's theorem

In his paper on the Mordell-Lang conjecture, Hrushovski employed techniques from model theory to prove the function field version of the conjecture. In doing so he was able to answer a related question of Voloch, which we refer to henceforth as Hrushovski's theorem. In this paper we shall give an alternative proof of said theorem in the characteristic $p$ setting, but using purely algebro-geometric ideas.

math.AG↗
arXiv2026

Conifold gap and all-genus mirror symmetry for local $\mathbb{P}^2$

The Conifold Gap Conjecture asserts that the polar part of the Gromov-Witten potential of a Calabi-Yau threefold near its conifold locus has a universal expression described by the logarithm of the Barnes $G$-function. In this paper, I prove the Conifold Gap Conjecture for the local projective plane. The proof relates the higher genus conifold Gromov-Witten generating series of local $\mathbb{P}^2$ to the thermodynamics of a certain statistical mechanical ensemble of repulsive particles on the positive half-line. As a corollary, this establishes the all-genus mirror principle for local $\mathbb{P}^2$ through the direct integration of the BCOV holomorphic anomaly equations.

math.AG↗