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Helix structures in quantum cohomology of fano varieties

Record Type:	Electronic resources : Monograph/item
Title/Author:	Helix structures in quantum cohomology of fano varietiesby Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti.
Author:	Cotti, Giordano.
other author:	Dubrovin, B. A.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xiii, 236 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Helices (Algebraic topology)
Online resource:	https://doi.org/10.1007/978-3-031-69067-9
ISBN:	9783031690679$q(electronic bk.)

Helix structures in quantum cohomology of fano varieties
Cotti, Giordano.

Helix structures in quantum cohomology of fano varieties[electronic resource] /by Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti. - Cham :Springer Nature Switzerland :2024. - xiii, 236 p. :ill. (chiefly color), digital ;24 cm. - Lecture notes in mathematics,v. 23561617-9692 ;. - Lecture notes in mathematics ;2035..

- 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.

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.

ISBN: 9783031690679$q(electronic bk.)

Standard No.: 10.1007/978-3-031-69067-9doiSubjects--Topical Terms:

984450
Helices (Algebraic topology)

LC Class. No.: QA612.3

Dewey Class. No.: 514.23

Helix structures in quantum cohomology of fano varieties
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505 0 $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.
520 $a 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.
650 0 $a Helices (Algebraic topology) $3 984450
650 0 $a Homology theory. $3 205880
650 0 $a Coherent analytic sheaves. $3 984451
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Mathematical Physics. $3 522725
650 2 4 $a Differential Equations. $3 285983
650 2 4 $a Differential Geometry. $3 273785
650 2 4 $a Category Theory, Homological Algebra. $3 275954
700 1 $a Dubrovin, B. A. $3 984448
700 1 $a Guzzetti, Davide. $3 984449
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