Helix Structures in Quantum Cohomology of Fano Varieties | Agenda Bookshop Skip to content
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A01=Boris A. Dubrovin
A01=Davide Guzzetti
A01=Giordano Cotti
Age Group_Uncategorized
Age Group_Uncategorized
Author_Boris A. Dubrovin
Author_Davide Guzzetti
Author_Giordano Cotti
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Category1=Non-Fiction
Category=PBF
Category=PBKJ
Category=PBMP
Category=PBMW
Category=PHU
COP=Switzerland
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Language_English
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Price_€50 to €100
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Helix Structures in Quantum Cohomology of Fano Varieties

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 -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.

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A01=Boris A. DubrovinA01=Davide GuzzettiA01=Giordano CottiAge Group_UncategorizedAuthor_Boris A. DubrovinAuthor_Davide GuzzettiAuthor_Giordano Cottiautomatic-updateCategory1=Non-FictionCategory=PBFCategory=PBKJCategory=PBMPCategory=PBMWCategory=PHUCOP=SwitzerlandDelivery_Pre-orderLanguage_EnglishPA=Not yet availablePrice_€50 to €100PS=Forthcomingsoftlaunch

Will deliver when available. Publication date 02 Dec 2024

Product Details
  • Dimensions: 155 x 235mm
  • Publication Date: 02 Dec 2024
  • Publisher: Springer International Publishing AG
  • Publication City/Country: Switzerland
  • Language: English
  • ISBN13: 9783031690662

About Boris A. DubrovinDavide GuzzettiGiordano Cotti

Davide 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 (19502019) 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 (19881993) and at SISSA from 1993 to 2019.

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