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