2005/06/29 by Daniel Hernández Ruipérez, Ruiperez, D. Hernandez, Ana Cristina López Martín +3 · 1 citation
Mathematics · #13D22 #14E30 #14F05 #14J27 #14M05 (Secondary) #18E30 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.math/0506593
openalex publication_date 2005/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend to singular schemes with Gorenstein singularities or fibered in schemes of that kind Bondal and Orlov's criterion for an integral functor to be fully faithful. We also contemplate a criterion for equivalence. We offer a proof that is new even if we restrict to the smooth case. In addition, we prove that for locally projective Gorenstein morphisms, a relative integral functor is fully faithful if and only if its restriction to each fibre also is it. These results imply the invertibility of the usual relative Fourier-Mukai transform for an elliptic fibration as a direct corollary.