17 citations · 77 across the 18 of their papers we have counts for
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Quasi-algebraic quantization for the B-twist Langlands TQFT
Eric Yen-Yo Chen, Emilio Franco
This is the first part of a program to construct hyperholomorphic families of boundary conditions for the Kapustin--Witten B-twist of the Langlands QFT, otherwise known as \textit{…
Fourier-Mukai transforms and normalisation of nodal curves
Emilio Franco, Robert Hanson, Johannes Horn +1
We study Arinkin's Poincaré sheaf on the singular locus of , the compactified Jacobian of rank one torsion-free sheaves on an integral no…
The Dirac-Higgs complex and categorification of (BBB)-branes
Emilio Franco, Robert Hanson
Let denote the hyperkähler moduli space of -Higgs bundles over a smooth projective curve . In the context of four dimensional supersymmetric…
Narasimhan--Ramanan branes and wobbly Higgs bundles
Emilio Franco, Peter B. Gothen, André G. Oliveira +1
Narasimhan--Ramanan branes were introduced by the authors in a previous article. They consist of a family of -branes inside the moduli space of Higgs bundles, and a family of…
O'Grady spaces and symplectic resolution of moduli spaces of Higgs bundles
Emilio Franco
We describe here a degeneration of the symplectic desingularization of the moduli spaces of topologically trivial and -Higgs bundles over a hyp…
Fourier-Mukai transform for fine compactified Prym varieties
Emilio Franco, Robert Hanson, João Ruano
Consider a finite covering of a smooth projective curve by a reduced, projective, planar curve . Associated to two general polarizations on , and , o…
Degeneration of natural Lagrangians and Prymian integrable systems
Emilio Franco
Starting from an anti-symplectic involution on a K3 surface, one can consider a natural Lagrangian subvariety inside the moduli space of sheaves over the K3. One can also construct…
Deformation theory of orthogonal and symplectic sheaves
Emilio Franco
We show that the space of first-order deformations of an orthogonal (resp. symplectic) sheaf over a smooth projective scheme is the first hypercohomology space of a complex which i…
Unramified covers and branes on the Hitchin system
Emilio Franco, Peter Gothen, André Oliveira +1
We study the locus of the moduli space of Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under an unramified cover. We equip these loci with a hyperh…
Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups
Emilio Franco, Ana Peón-Nieto
We study mirror symmetry on the singular locus of the Hitchin system at two levels. Firstly, by covering it by (supports of) -branes, corresponding to Higgs bundles reducing…
Mirror symmetry for Nahm branes
Emilio Franco, Marcos Jardim
The Dirac--Higgs bundle is a hyperholomorphic bundle over the moduli space of stable Higgs bundles of coprime rank and degree. We provide an algebraic generalization to the case of…
Involutions of the moduli spaces of -Higgs bundles over elliptic curves
Indranil Biswas, Luis Angel Calvo, Emilio Franco +1
We present a systematic study of involutions on the moduli space of -Higgs bundles over an elliptic curve , where is complex reductive affine algebraic group. The fixed p…
Brane involutions on irreducible holomorphic symplectic manifolds
Emilio Franco, Marcos Jardim, Grégoire Menet
In the context of irreducible holomorphic symplectic manifolds, we say that (anti)holomorphic (anti)symplectic involutions are brane involutions since their fixed point locus is a…
Higgs bundles over elliptic curves for real groups
Emilio Franco, Óscar García-Prada, P. E. Newstead
We study topologically trivial -Higgs bundles over an elliptic curve when the structure group is a connected real form of a complex semisimple Lie group …
Moduli spaces of -modules on abelian varieties
Emilio Franco, Pietro Tortella
We study the moduli space of semistable -modules of vanishing Chern classes over an abelian variety , where belongs to a certain subclass of -alge…
Branes in the moduli space of framed instantons
Emilio Franco, Marcos Jardim, Simone Marchesi
In the physicist's language, a brane in a hyperkahler manifold is a submanifold which is either complex or lagrangian with respect to three Kahler structures of the ambient manif…
Higgs bundles over elliptic curves for complex reductive Lie groups
Emilio Franco, Oscar Garcia-Prada, P. E. Newstead
We study Higgs bundles over an elliptic curve with complex reductive structure group, describing the (normalization of) its moduli spaces and the associated Hitchin fibration. The…
Higgs bundles over elliptic curves
Emilio Franco, Oscar Garcia-Prada, P. E. Newstead
In this paper we study -Higgs bundles over an elliptic curve when the structure group is a classical complex reductive Lie group. Modifying the notion of family, we define a…