2023/01/31 by Bu, Chenjing
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2302.00038
In this series of papers, we propose a theory of enumerative invariants counting self-dual objects in self-dual categories. Ordinary enumerative invariants in abelian categories can be seen as invariants for the structure group GL (n), and our theory is an extension of this to structure groups O (n) and Sp (2n). Examples of our invariants include invariants counting principal orthogonal or symplectic bundles, and invariants counting self-dual quiver representations. In the present paper, we take the motivic approach, and define our invariants as elements in a ring of motives. We also extract numerical invariants by taking Euler characteristics of these elements. We prove wall-crossing formulae relating our invariants for different stability conditions. We also provide an explicit algorithm computing invariants for quiver representations, and we present some numerical results.