Helix Structures in Quantum Cohomology of Fano Varieties

Giordano Cotti (u. a.)

ISBN 10: 3031690664 / ISBN 13: 9783031690662

Published by Springer, 2024

About this Item

Helix Structures in Quantum Cohomology of Fano Varieties | Giordano Cotti (u. a.) | Taschenbuch | Lecture Notes in Mathematics | xiii | Englisch | 2024 | Springer | EAN 9783031690662 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

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Bibliographic Details

• Title: Helix Structures in Quantum Cohomology of Fano Varieties
• Publisher: Springer
• Publication Date: 2024
• Language: English
• ISBN 10: 3031690664
• ISBN 13: 9783031690662
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 14D millimeters 235 millimeters width by 155 millimeters height by 14 millimeters depth
• Weight: 388 grams
• Seller catalogs:
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About this title

Synopsis

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.

About the Author

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 (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.