Related papers: Quantization of spectral curves and DQ-modules

In this paper we consider a canonical compactification of Hitchin's moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface, producing a projective variety by gluing in a divisor at infinity. We give…

In this paper, we investigate the geometry of the base complex manifold of an effectively parametrized holomorphic family of stable Higgs bundles over a fixed compact K\"{a}hler manifold. The starting point of our study is…

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define…

We prove a homological characterization of $Q$-manifolds bundles over $C$-spaces. This provides a partial answer to Question QM22 from \cite{w}.

We introduce the notions of deformation Higgs bundle and Riemann-Finsler metric on the moduli space of polarized varieties. We also use the Higgs-de Rham flow in the p-adic setting. These are the key novelties in our program.

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…

The Quillen connection on ${\mathcal L} \rightarrow {\mathcal M}_g$, where ${\mathcal L}^*$ is the Hodge line bundle over the moduli stack of smooth complex projective curves curves ${\mathcal M}_g$, $g \geq 5$, is uniquely determined by…

We derive the spectral curves for $q$-part double Hurwitz numbers, $r$-spin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0,1)-geometry. We quantize this family of spectral curves and…

We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus g, defined over a finite field, when the degree of the twisting line bundle is at least…

We give a differential geometric construction of the holomorphic family of Higgs bundle moduli spaces over a curve C as a fibration over Teichm\"uller space. The method uses a function f defined on the character variety, essentially the…

We investigate the geometric and conformally equivariant quantizations of the supercotangent bundle of a pseudo-Riemannian manifold $(M,g)$, which is a model for the phase space of a classical spin particle. This is a short review of our…

Let $\Oq(G)$ be the algebra of quantized functions on an algebraic group $G$ and $\Oq(B)$ its quotient algebra corresponding to a Borel subgroup $B$ of $G$. We define the category of sheaves on the "quantum flag variety of $G$" to be the…

Through the action of anti-holomorphic involutions on a compact Riemann surface, we construct families of (A,B,A)-branes in the moduli spaces of G_c-Higgs bundles on the Riemann surface. We study the geometry of these (A,B,A)-branes in…

We introduce a new moduli stack $\mathscr{E}_{g,n}$ of ``equinormalized curves," closely related to the moduli space of all reduced, connected algebraic curves. We construct a stratification $\bigsqcup_\Gamma \mathscr{E}_\Gamma$ of…

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

We show the existence of a symplectic structure on the moduli space of the Seiberg-Witten equations on $\Sigma \times \Sigma$ where $\Sigma$ is a compact oriented Riemann surface. To prequantize the moduli space, we construct a Quillen-type…

A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…

In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The…

Let P be a parabolic subgroup of a simple affine algebraic group G defined over C and X a compact connected K\"ahler manifold. L. \'Alvarez-C\'onsul and O. Garc\'ia-Prada associated to these a quiver Q and representations of Q into…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…