2019/02/01 by Bejleri, Dori, Inchiostro, Giovanni · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.00504
We propose an alternative definition for families of stable pairs (X,D) over a possibly non-reduced base when D is reduced, by replacing (X,D) with an appropriate orbifold pair (\mathcal X,\mathcal D). This definition of a stable family ends up being equivalent to previous ones, but has the advantage of being more amenable to the tools of deformation theory. Moreover, adjunction for (\mathcal X,\mathcal D) holds on the nose; there is no correction term coming from the different. This leads to the existence of functorial gluing morphisms for families of stable surfaces and functorial morphisms from (n + 1) dimensional stable pairs to n dimensional polarized orbispace. As an application, we study the deformation theory of some surface pairs.