@article {2013, title = {Monads for framed sheaves on Hirzebruch surfaces}, number = {SISSA preprint;05/2014/mate}, year = {2013}, abstract = {We define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.}, keywords = {Monads, framed sheaves, Hirzebruch surfaces}, author = {Claudio Bartocci and Ugo Bruzzo and Claudio L.S. Rava} } @article {2010, title = {On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system}, journal = {Int. Math. Res. Not. (2010) 2010:279-296}, number = {arXiv.org;0902.0953v2}, year = {2010}, publisher = {Oxford University Press}, abstract = {We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.}, doi = {10.1093/imrn/rnp130}, url = {http://hdl.handle.net/1963/3800}, author = {Claudio Bartocci and Gregorio Falqui and Igor Mencattini and Giovanni Ortenzi and Marco Pedroni} } @article {2004, title = {A geometric approach to the separability of the Neumann-Rosochatius system}, journal = {Differential Geom. Appl. 21 (2004) 349-360}, number = {arXiv.org;nlin/0307021}, year = {2004}, abstract = {We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.}, doi = {10.1016/j.difgeo.2004.07.001}, url = {http://hdl.handle.net/1963/2541}, author = {Claudio Bartocci and Gregorio Falqui and Marco Pedroni} } @article {2002, title = {Relatively stable bundles over elliptic fibrations}, journal = {Math. Nachr. 238 (2002) 23-36}, number = {arXiv.org;math/0109123v2}, year = {2002}, publisher = {Wiley}, abstract = {We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah\\\'s and Tu\\\'s results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.}, url = {http://hdl.handle.net/1963/3132}, author = {Claudio Bartocci and Ugo Bruzzo and Daniel Hernandez Ruiperez and Jose M. Munoz Porras} } @article {1999, title = {Categorial mirror symmetry for K3 surfaces}, journal = {Comm. Math. Phys. 206 (1999) 265-272}, number = {SISSA;100/98/FM/GEO}, year = {1999}, publisher = {Springer}, abstract = {We study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$.}, doi = {10.1007/s002200050705}, url = {http://hdl.handle.net/1963/2887}, author = {Claudio Bartocci and Ugo Bruzzo and Guido Sanguinetti} } @article {1990, title = {Chern-Simons forms on principal superfiber bundles}, journal = {J.Math.Phys.31:45,1990}, number = {SISSA;109/87/FM}, year = {1990}, publisher = {SISSA Library}, abstract = {A graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a {\textquoteleft}{\textquoteleft}superextension\\\'\\\' of the Dirac monopole is discussed.}, doi = {10.1063/1.528826}, url = {http://hdl.handle.net/1963/590}, author = {Giovanni Landi and Claudio Bartocci and Ugo Bruzzo} }