ICTP/IGAP seminar on Algebraic Geometry:Representations of the diagonal for moduli spaces of sheaves

ICTP/IGAP seminar on Algebraic Geometry: Representations of the diagonal for moduli spaces of sheaves

Speaker: Alina MARIAN (Northeastern University)

Toward the cohomology and Chow rings of moduli spaces of sheaves (Alina Marian)

A seminar direction will examine the problem of understanding Lie algebra actions on the cohomology and Chow rings of moduli spaces of sheaves interms of the Chern classes of the universal sheaf. One classical action on cohomology is the Lefschetz sl(2) associated with an ample divisor class on a projective variety. For moduli spaces of sheaves over curves and surfaces, Grothendieck's standard conjectures are often known to hold, in particular Lefschetz sl(2) actions should be expressible via algebraic correspondences. Nevertheless there are very few explicit algebraic constructions of the Lefschetz operators. Progress in this direction would have important applications, not least to holomorphic symplectic geometry; the seminar will explain this circle of ideas.