LEADER 04108nam 22008295 450 001 9910900176303321 005 20260121103912.0 010 $a3-031-69067-2 024 7 $a10.1007/978-3-031-69067-9 035 $a(MiAaPQ)EBC31743913 035 $a(Au-PeEL)EBL31743913 035 $a(CKB)36414867500041 035 $a(DE-He213)978-3-031-69067-9 035 $a(PPN)281459835 035 $a(EXLCZ)9936414867500041 100 $a20241029d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHelix Structures in Quantum Cohomology of Fano Varieties /$fby Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (241 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2356 311 08$a3-031-69066-4 327 $a- 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. 330 $aThis research monograph provides a comprehensive study of a conjecture initially proposed by the second author at the 1998 International Congress of Mathematicians (ICM). This conjecture asserts the equivalence, for a Fano variety, between the semisimplicity condition of its quantum cohomology and the existence of full exceptional collections in its derived category of coherent sheaves. Additionally, in its quantitative form, the conjecture specifies an explicit relation between the monodromy data of the quantum cohomology, characteristic classes, and exceptional collections. A refined version of the conjecture is introduced, with a particular focus on the central connection matrix, and a precise link is established between this refined conjecture and ?-conjecture II, as proposed by S. Galkin, V. Golyshev, and H. Iritani. By performing explicit calculations of the monodromy data, the validity of the refined conjecture for all complex Grassmannians G(r,k) is demonstrated. Intended for students and researchers, the book serves as an introduction to quantum cohomology and its isomonodromic approach, along with its algebraic counterpart in the derived category of coherent sheaves. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2356 606 $aGeometry, Algebraic 606 $aMathematical physics 606 $aDifferential equations 606 $aGeometry, Differential 606 $aAlgebra, Homological 606 $aAlgebraic Geometry 606 $aMathematical Physics 606 $aDifferential Equations 606 $aDifferential Geometry 606 $aCategory Theory, Homological Algebra 606 $aCategories (Matemàtica)$2thub 606 $aGeometria algebraica$2thub 606 $aTopologia algebraica$2thub 606 $aHomologia$2thub 606 $aHèlices$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry, Algebraic. 615 0$aMathematical physics. 615 0$aDifferential equations. 615 0$aGeometry, Differential. 615 0$aAlgebra, Homological. 615 14$aAlgebraic Geometry. 615 24$aMathematical Physics. 615 24$aDifferential Equations. 615 24$aDifferential Geometry. 615 24$aCategory Theory, Homological Algebra. 615 7$aCategories (Matemàtica) 615 7$aGeometria algebraica 615 7$aTopologia algebraica 615 7$aHomologia 615 7$aHèlices 676 $a516.35 700 $aCotti$b Giordano$01767776 701 $aDubrovin$b Boris A$052477 701 $aGuzzetti$b Davide$01767777 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910900176303321 996 $aHelix Structures in Quantum Cohomology of Fano Varieties$94214074 997 $aUNINA