I am Armando and am interested to complex geometry, in particular:
- positivity conditions for vector and principal (Higgs) bundles;
- moduli spaces of Higgs bundles;
- Hilbert functions of 0-dimensional schemes;
- weak Lefschetz properties for Artinian graded algebras.
I'm intrigued by:
- Dolbeault moduli spaces;
- cohomology of compact Kähler spaces (compact, complex, reduced analytic spaces with a Kähler form);
- singularites of (Poincaré) normal functions;
- complex projective varieties with Hessian indeterminated;
- counting curves and sheaves on K3 surfaces;
- Hopf algebra cohomology.