03703nam 22006975 450 991090017630332120250808090310.03-031-69067-210.1007/978-3-031-69067-9(MiAaPQ)EBC31743913(Au-PeEL)EBL31743913(CKB)36414867500041(DE-He213)978-3-031-69067-9(PPN)281459835(EXLCZ)993641486750004120241029d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierHelix Structures in Quantum Cohomology of Fano Varieties /by Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (241 pages)Lecture Notes in Mathematics,1617-9692 ;23563-031-69066-4 - Introduction -- Gromov–Witten Theory and Quantum Cohomology -- Helix Theory in Triangulated Categories -- Non-Symmetric Orthogonal Geometry of Mukai Lattices -- The Main Conjecture -- Proof of the Main Conjecture for Projective Spaces -- Proof of the Main Conjecture for Grassmannians.This research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM). This conjecture asserts the equivalence, for a Fano variety, between the semisimplicity condition of its quantum cohomology and the existence of full exceptional collections in its derived category of coherent sheaves. Additionally, in its quantitative form, the conjecture specifies an explicit relation between the monodromy data of the quantum cohomology, characteristic classes, and exceptional collections. A refined version of the conjecture is introduced, with a particular focus on the central connection matrix, and a precise link is established between this refined conjecture and Γ-conjecture II, as proposed by S. Galkin, V. Golyshev, and H. Iritani. By performing explicit calculations of the monodromy data, the validity of the refined conjecture for all complex Grassmannians G(r,k) is demonstrated. Intended for students and researchers, the book serves as an introduction to quantum cohomology and its isomonodromic approach, along with its algebraic counterpart in the derived category of coherent sheaves.Lecture Notes in Mathematics,1617-9692 ;2356Geometry, AlgebraicMathematical physicsDifferential equationsGeometry, DifferentialAlgebra, HomologicalAlgebraic GeometryMathematical PhysicsDifferential EquationsDifferential GeometryCategory Theory, Homological AlgebraGeometry, Algebraic.Mathematical physics.Differential equations.Geometry, Differential.Algebra, Homological.Algebraic Geometry.Mathematical Physics.Differential Equations.Differential Geometry.Category Theory, Homological Algebra.516.35Cotti Giordano1767776Dubrovin Boris A52477Guzzetti Davide1767777MiAaPQMiAaPQMiAaPQBOOK9910900176303321Helix Structures in Quantum Cohomology of Fano Varieties4214074UNINA