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.

}, 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 = {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 $\tilde{\mathcal{N}}\ \rightarrow \mathcal{M}$, 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.

}, 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} }