|
|
|||
|
||||
OverviewThis 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. Full Product DetailsAuthor: Davide Guzzetti , Giordano Cotti , Boris A. DubrovinPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 2024 ed. Volume: 2356 ISBN: 9783031690662ISBN 10: 3031690664 Pages: 236 Publication Date: 25 November 2024 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Forthcoming Availability: Not yet available This item is yet to be released. You can pre-order this item and we will dispatch it to you upon its release. Table of ContentsReviewsAuthor InformationDavide Guzzetti obtained his Ph.D. in Mathematical Physics in 2000 from the Scuola Internazionale Superiore di Studi Avanzati SISSA, Trieste, Italy. After holding research positions at RIMS, Kyoto University, Japan, and KIAS, Seoul, South Korea, he became a researcher at SISSA in 2011, and an associate professor in 2018. Giordano Cotti obtained his Ph.D. in Geometry and Mathematical Physics from SISSA in 2017. He has held research positions at the Max Planck Institute for Mathematics in Bonn, Germany, and the University of Birmingham in the UK. Since 2020, he has been a researcher in the Group of Mathematical Physics at the University of Lisbon in Portugal. Boris A. Dubrovin (1950–2019) obtained his Ph.D. in Geometry and Topology at Moscow State University under the supervision of S.P. Novikov. After obtaining his Habilitation in 1984, he was a full professor at Moscow State University (1988–1993) and at SISSA from 1993 to 2019. Tab Content 6Author Website:Countries AvailableAll regions |