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Helix structures in quantum cohomology of fano varieties

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Helix structures in quantum cohomology of fano varieties/ by Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti.
作者:	Cotti, Giordano.
其他作者:	Guzzetti, Davide.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xiii, 236 p. :ill. (chiefly color), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Category Theory, Homological Algebra. -
電子資源:	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:

678397
Category Theory, Homological Algebra.

LC Class. No.: QA612.3

Dewey Class. No.: 514.23

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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.
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