2021/07/05 by Daniel Halpern-Leistner, Halpern-Leistner, Daniel, Andres Fernandez Herrero +3 · 1 citation
Mathematics · #14D23 (Primary) 14J60 #14F06 #14L24 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2107.02172
openalex publication_date 2021/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two familiar moduli problems: the stack of Λ-modules and the stack of pairs. In both examples, we construct a Θ-stratification of the stack, defined in terms of a polynomial numerical invariant, and we construct good moduli spaces for the open substacks of semistable points. One of the essential ingredients is the construction of higher dimensional analogues of the affine Grassmannian for the moduli problems considered.