Virtual classes and virtual motives of Quot schemes on threefolds
Andrea T. Ricolfi
2020Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna)26 citationsDOIOpen Access PDF
Abstract
For a simple, rigid vector bundle F on a Calabi–Yau 3-fold Y, we construct a symmetric obstruction theory on the Quot scheme QuotY(F,n), and we solve the associated enumerative theory. We discuss the case of other 3-folds. Exploiting the critical structure on the local model QuotAjavax.xml.bind.JAXBElement@e117367(O⊕r,n), we construct a virtual motive (in the sense of Behrend–Bryan–Szendrői) for QuotY(F,n) for an arbitrary vector bundle F on a smooth 3-fold Y. We compute the associated motivic partition function. We obtain new examples of higher rank (motivic) Donaldson–Thomas invariants.
Topics & Concepts
Vector bundleMathematicsRank (graph theory)Scheme (mathematics)BundleConstruct (python library)Partition (number theory)Pure mathematicsPartition function (quantum field theory)Simple (philosophy)Algebra over a fieldCombinatoricsMathematical analysisComputer sciencePhilosophyProgramming languageMaterials scienceEpistemologyPhysicsQuantum mechanicsComposite materialAlgebraic Geometry and Number TheoryAdvanced Algebra and GeometryAlgebraic structures and combinatorial models