Bow varieties -- geometry, combinatorics, characteristic classes (Q6651628)

Assigning cohomology classes to geometrically relevant subsets of a variety is an effective technique in enumerative algebraic geometry. The prototype is the assignment of Schubert classes to the Schubert varieties of a Grassmannian. The study of these classes, e.g., their multiplicative properties, their combinatorics, their relation to representation theory and algebraic combinatorics, is an important part of Schubert calculus.\N\NCherkis bow varieties are believed to be the set of spaces where 3-dimensional mirror symmetry for characteristic classes can be observed. The authors describe geometric structures on a large class of Cherkis bow varieties by developing the necessary combinatorial presentations, including binary contingency tables and skein diagrams. They take the first steps toward the sought after statement for 3-dimensional mirror symmetry for characteristic classes by conjecturing a formula for cohomological stable envelopes. Additionally they provide an account of the full statement, with examples, for elliptic stable envelopes.