activity
20062026
most citedAlgebraic Nahm transform for Parabolic Higgs Bundles on P^1

7 citations · 17 across the 9 of their papers we have counts for

collaborators

12 papers

math.AG2026

Moduli of atoms of complex projective varieties

Maxim Kontsevich, Szilard Szabo

The category of constituent pieces of Dubrovin connection of varieties is introduced and shown to be representable in affine space.

math.AG2024

Floer-theoretic filtration on Painlevé Hitchin systems

Szilárd Szabó, Filip Živanović

We classify equivariant -actions on moduli spaces of Higgs bundles corresponding to the Painlevé equations. Using this, we compute the Floer-theoretic filtrations on…

math.DG2023★ 1 cited

Asymptotic behaviour of large-scale solutions of Hitchin's equations in higher rank

Takuro Mochizuki, Szilárd Szabó

Let be a compact Riemann surface. Let be a stable Higgs bundle of degree on . Let denote a flat metric of the determinant bundle . For any…

math.AG2022

Blow-ups and the quantum spectrum of surfaces

Ádám Gyenge, Szilárd Szabó

We investigate the behaviour of the spectrum of the quantum (or Dubrovin) connection of smooth projective surfaces under blow-ups. Our main result is that for small values of the p…

math.AG2020★ 4 cited

The Geometric P=W conjecture in the Painlevé cases via plumbing calculus

András Némethi, Szilárd Szabó

We use plumbing calculus to prove the homotopy commutativity assertion of the Geometric P=W conjecture in all Painlevé cases. We discuss the resulting Mixed Hodge structures on Dol…

math.AG2018★ 1 cited

Perversity equals weight for Painlevé spaces

Szilárd Szabó

We provide further evidence to the conjecture of de Cataldo, Hausel and Migliorini, by checking it in the Painlevé cases. Namely, we compare the perverse Leray filtration ind…

math.AG2017

Hitchin fibrations on moduli of irregular Higgs bundles and motivic wall-crossing

Péter Ivanics, András I. Stipsicz, Szilárd Szabó

In this paper we give a complete description of the Hitchin fibration on all 2-dimensional moduli spaces of rank 2 irregular Higgs bundles with two poles on the projective line. We…

math.AG2017

Nahm transformation for parabolic integrable connections on the projective line -- case of generic regular graded residues

Szilárd Szabó

We give a de Rham interpretation of Nahm's transform for certain parabolic harmonic bundles on the projective line and compare it to minimal Fourier--Laplace transform of $\mathcal…

math.CO2016

Normal forms of endomorphism-valued power series

Christopher Keane, Szilárd Szabó

We show for , and an -dimensional complex vector space that if an element has constant term similar to a Jordan block, then there exists a…

math.AG2016★ 4 cited

Two-dimensional moduli spaces of irregular Higgs bundles

Péter Ivanics, András I. Stipsicz, Szilárd Szabó

We give a complete description of the two-dimensional moduli spaces of stable Higgs bundles of rank 2 over complex projective line with one irregular singular point, having a regul…

math.DG2011

Deformation theory of Fuchsian equations and logarithmic connections

Szilárd Szabó

Motivated by a remark and a question of Nicholas Katz, we characterize the tangent space of the space of Fuchsian equations with given generic exponents inside the corresponding mo…

math.AG2006★ 7 cited

Algebraic Nahm transform for Parabolic Higgs Bundles on P^1

K. Aker, Sz. Szabo

We study Nahm transformation for parabolic Higgs bundles on the projective line \PP^1, with logarithmic singularities on a finite set P. Such a Higgs bundle can be given by its spe…