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Fix integers $ggeq 3$ and $rgeq 2$, with $rgeq 3$ if $g=3$. Given a compact connected Riemann surface $X$ of genus $g$, let $MDH(X)$ denote the corresponding $text{SL}(r, {mathbb C})$ Deligne--Hitchin moduli space. We prove that the complex analytic space $MDH(X)$ determines (up to an isomorphism) the unordered pair ${X, overline{X}}$, where $overline{X}$ is the Riemann surface defined by the opposite almost complex structure on $X$.
Let X be an irreducible smooth complex projective curve of genus g>2, and let x be a fixed point. A framed bundle is a pair (E,phi), where E is a vector bundle over X, of rank r and degree d, and phi:E_xto C^r is a non-zero homomorphism. There is a n
In this article we extend the proof given by Biswas and Gomez of a Torelli theorem for the moduli space of Higgs bundles with fixed determinant, to the parabolic situation.
A conjectural recursive relation for the Poincare polynomial of the Hitchin moduli space is derived from wallcrossing in the refined local Donaldson-Thomas theory of a curve. A doubly refined generalization of this theory is also conjectured and show
In this paper, we generalize the construction of Deligne-Hitchin twistor space by gluing two certain Hodge moduli spaces. We investigate such generalized Deligne-Hitchin twistor space as a complex analytic manifold, more precisely, we show it admits
Given two semistable, non potentially isotrivial elliptic surfaces over a curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the N{e}ron-Seve