2024/01/21 by Yuto Arai, Arai, Yuto
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2401.11503
openalex publication_date 2024/01/21 · openalex created_date 2024/01/24 · openalex updated_date 2026/07/28
We develop the method of inducing semiorthogonal decompositions of projective varieties with isolated rational singularities from those of small resolutions of singularities, which generalizes semiorthogonal decompositions for singular surfaces by Karmazyu-Kuznetsov-Shinder. \par We first explain the classical generator of the null category, which is a kind of triangulated full subcategory, and prove that the orthogonal decompositions of the null category is induced through its generator. Next, we prove that the candidate of induced semiorthogonal decomposition behaves well with respect to the inverse image of resolution morphism, and as a corollary, we obtain the required semiorthogonal decomposition.