2022/10/16 by Benjamin Sung, Sung, Benjamin
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2210.08637
We prove that any non-commutative smooth projective variety with a Bridgeland stability condition of dimension less than (6)/(5) must be a smooth projective curve. As a consequence, we deduce the non-existence of such categories with dimension in the interval (1,(6)/(5)). Moreover, we prove a sharp reconstruction result for smooth projective curves of higher genus using the moduli space of stable objects in a category of dimension 1, and deduce a structural result for their semi-orthogonal decompositions.