Fr. 95.20

Helix Structures in Quantum Cohomology of Fano Varieties

English · Paperback / Softback

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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.

List of contents

- 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.

Product details

Authors Giordano Cotti, Boris A Dubrovin, Boris A. Dubrovin, Davide Guzzetti
Publisher Springer, Berlin
 
Languages English
Product format Paperback / Softback
Released 01.10.2024
 
EAN 9783031690662
ISBN 978-3-0-3169066-2
No. of pages 236
Dimensions 155 mm x 13 mm x 235 mm
Weight 388 g
Illustrations XIII, 236 p. 18 illus., 15 illus. in color.
Series Lecture Notes in Mathematics
Subject Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra

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