@article {2009,
	title = {Gauged Laplacians on quantum Hopf bundles},
	journal = {Comm. Math. Phys. 287 (2009) 179-209},
	number = {arXiv.org;0801.3376v2},
	year = {2009},
	publisher = {Springer},
	abstract = {We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe {\textquoteleft}excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.},
	doi = {10.1007/s00220-008-0672-5},
	url = {http://hdl.handle.net/1963/3540},
	author = {Giovanni Landi and Cesare Reina and Alessandro Zampini}
}
@article {2008,
	title = {Noncommutative families of instantons},
	journal = {Int. Math. Res. Not. vol. 2008, Article ID rnn038},
	number = {arXiv.org;0710.0721v2},
	year = {2008},
	publisher = {Oxford University Press},
	abstract = {We construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.},
	doi = {10.1093/imrn/rnn038},
	url = {http://hdl.handle.net/1963/3417},
	author = {Giovanni Landi and Chiara Pagani and Cesare Reina and Walter van Suijlekom}
}
@article {2006,
	title = {A Hopf bundle over a quantum four-sphere from the symplectic group},
	journal = {Commun. Math. Phys. 263 (2006) 65-88},
	number = {arXiv.org;math/0407342v2},
	year = {2006},
	abstract = {We construct a quantum version of the SU(2) Hopf bundle $S^7 \\\\to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4-sphere $S^4_q$ is obtained via a suitable self-adjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$-homology class of $S^4_q$ and pair it with the class of $p$ in the $K$-theory getting the value -1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$.},
	doi = {10.1007/s00220-005-1494-3},
	url = {http://hdl.handle.net/1963/2179},
	author = {Giovanni Landi and Chiara Pagani and Cesare Reina}
}
@article {2003,
	title = {Quantum spin coverings and statistics},
	journal = {J. Phys. A 36 (2003), no. 13, 3829-3840},
	number = {SISSA;97/2002/FM},
	year = {2003},
	publisher = {IOP Publishing},
	abstract = {SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.},
	doi = {10.1088/0305-4470/36/13/314},
	url = {http://hdl.handle.net/1963/1667},
	author = {Ludwik Dabrowski and Cesare Reina}
}
@article {2001,
	title = {A note on the super Krichever map},
	journal = {J. Geom. Phys. 37 (2001), no. 1-2, 169-181},
	number = {SISSA;36/00/FM},
	year = {2001},
	publisher = {SISSA Library},
	abstract = {We consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based\\non the Fa{\textquoteleft}a di Bruno recursion relations, considered as the cocycle condition for the natural double complex associated with the deformations of super Krichever data. Our approach is based on the construction of the universal super divisor (of degree g), and a local universal family of geometric data which give the map into the Super Grassmannian.},
	doi = {10.1016/S0393-0440(00)00037-1},
	url = {http://hdl.handle.net/1963/1494},
	author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa}
}
@article {2000,
	title = {3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3},
	journal = {Nucl.Phys. B577 (2000) 547-608},
	number = {SISSA;113/99/FM},
	year = {2000},
	publisher = {SISSA Library},
	doi = {10.1016/S0550-3213(00)00098-5},
	url = {http://hdl.handle.net/1963/1327},
	author = {Davide Fabbri and Pietro Fr{\'e} and Leonardo Gualtieri and Cesare Reina and Alessandro Tomasiello and Alberto Zaffaroni and Alessandro Zampa}
}
@article {2000,
	title = {A(SLq(2)) at roots of unity is a free module over A(SL(2))},
	journal = {Lett. Math. Phys., 2000, 52, 339},
	number = {SISSA;42/00/FM},
	year = {2000},
	publisher = {SISSA Library},
	doi = {10.1023/A:1007601131002},
	url = {http://hdl.handle.net/1963/1500},
	author = {Ludwik Dabrowski and Cesare Reina and Alessandro Zampa}
}
@article {2000,
	title = {Super KP equations and Darboux transformations: another perspective on the Jacobian super KP hierarchy},
	journal = {J. Geom. Phys. 35 (2000), no. 2-3, 239-272},
	number = {SISSA;152/99/FM},
	year = {2000},
	publisher = {SISSA Library},
	doi = {10.1016/S0393-0440(00)00007-3},
	url = {http://hdl.handle.net/1963/1367},
	author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa}
}
@article {1999,
	title = {Enhanced gauge symmetries on elliptic K3},
	journal = {Phys.Lett. B452 (1999) 244-250},
	number = {SISSA;74/98/EP-FM},
	year = {1999},
	publisher = {Elsevier},
	abstract = {We show that the geometry of K3 surfaces with singularities of type A-D-E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3\\\'s.},
	doi = {10.1016/S0370-2693(99)00295-6},
	url = {http://hdl.handle.net/1963/3366},
	author = {Loriano Bonora and Cesare Reina and Alessandro Zampa}
}
@article {1997,
	title = {Krichever maps, Fa{\`a} di Bruno polynomials, and cohomology in KP theory},
	journal = {Lett. Math. Phys. 42 (1997) 349-361},
	number = {SISSA;37/97/FM},
	year = {1997},
	publisher = {Springer},
	abstract = {We study the geometrical meaning of the Faa\\\' di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faa\\\' di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.},
	doi = {10.1023/A:1007323118991},
	url = {http://hdl.handle.net/1963/3539},
	author = {Gregorio Falqui and Cesare Reina and Alessandro Zampa}
}
@inbook {1995,
	title = {Quantum homogeneous spaces at roots of unity},
	booktitle = {Quantization, Coherent States and Poisson Structures, Proc. XIVth Workshop on Geometric Methods in Physics, Bialowieza, Poland, 9-15 July 1995, eds. A. Strasburger,\\nS.T. Ali, J.-P. Antoine, J.-P. Gazeau , A. Odzijewicz, Polish Scientific Publisher PWN 1},
	number = {SISSA;120/95/FM},
	year = {1995},
	publisher = {SISSA Library},
	organization = {SISSA Library},
	url = {http://hdl.handle.net/1963/1022},
	author = {Cesare Reina and Alessandro Zampa}
}
@article {1993,
	title = {A Borel-Weil-Bott approach to representations of {\rm sl}\sb q(2,C)},
	journal = {Lett. Math. Phys. 29 (1993) 215-217},
	number = {SISSA;58/93/FM},
	year = {1993},
	publisher = {Springer},
	abstract = {<p>We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.</p>},
	doi = {10.1007/BF00761109},
	url = {http://hdl.handle.net/1963/3538},
	author = {Davide Franco and Cesare Reina}
}
@article {1992,
	title = {Topological "observables" in semiclassical field theories},
	journal = {Phys. Lett. B 297 (1992) 82-88},
	number = {arXiv.org;hep-th/9209096v1},
	year = {1992},
	publisher = {Elsevier},
	abstract = {<p>We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}}\&nbsp;\rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.</p>},
	doi = {10.1016/0370-2693(92)91073-I},
	url = {http://hdl.handle.net/1963/3541},
	author = {Margherita Nolasco and Cesare Reina}
}
@article {1990,
	title = {N=2 super Riemann surfaces and algebraic geometry},
	journal = {J. Math. Phys. 31 (1990), no.4, 948-952},
	number = {SISSA;47/89/FM},
	year = {1990},
	publisher = {American Institute of Physics},
	abstract = {The geometric framework for N=2 superconformal field theories are described by studying susy2 curves-a nickname for N=2 super Riemann surfaces. It is proved that \\\"single\\\'\\\' susy2 curves are actually split supermanifolds, and their local model is a Serre self-dual locally free sheaf of rank two over a smooth algebraic curve. Superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems.},
	doi = {10.1063/1.528775},
	url = {http://hdl.handle.net/1963/807},
	author = {Cesare Reina and Gregorio Falqui}
}
@article {1990,
	title = {A note on the global structure of supermoduli spaces},
	journal = {Comm.Math.Phys. 31 (1990), no.4, 948},
	number = {SISSA;46/89/FM},
	year = {1990},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/806},
	author = {Cesare Reina and Gregorio Falqui}
}
@article {1988,
	title = {Susy-curves and supermoduli},
	number = {SISSA;169/88/FM},
	year = {1988},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/761},
	author = {Gregorio Falqui and Cesare Reina}
}
