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Helix structures in quantum cohomology of fano varieties

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Helix structures in quantum cohomology of fano varieties/ by 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

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 ;1943..

- 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

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

1462201
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 1462201
650 0 $a Homology theory. $3 682984
650 0 $a Coherent analytic sheaves. $3 1462202
650 1 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Mathematical Physics. $3 786661
650 2 4 $a Differential Equations. $3 681826
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Category Theory, Homological Algebra. $3 678397
700 1 $a Dubrovin, B. A. $3 1462199
700 1 $a Guzzetti, Davide. $3 1462200
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