Cohomological Hall algebra of curves

31.03.2020 13:15 - 14:45

Olivier Schiffmann (Université de Paris-Sud)

Let X be a smooth projective curve and for any (r,d) let Coh_{r,d} stand for stack of coherent sheaves of rank r and degree d.

We equip the direct sum of cohomologies of all these stacks with an algebra structure (1d COHA). The rank zero part is identified with an explicit shuffle algebra, and its action on the higher rank part is given through some explicit vertex operators.

We give various ways of computing these products, and give several occurrences in enumerative geometry problems (such as the problem of determining the cohomology ring of the stacks of semistables sheaves).


H. Grobner, A. Minguez-Espallargas, A. Mellit

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