Helix Structures in Quantum Cohomology of Fano Varieties
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 t...
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|---|---|
| Байгууллагын зохиогч: | |
| Формат: | Цахим Цахим ном |
| Хэл сонгох: | англи |
| Хэвлэсэн: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Хэвлэл: | 1st ed. 2024. |
| Цуврал: | Lecture Notes in Mathematics,
2356 |
| Нөхцлүүд: | |
| Онлайн хандалт: | https://doi.org/10.1007/978-3-031-69067-9 |
| Шошгууд: |
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| 100 | 1 | |a Cotti, Giordano. |e author. |0 (orcid)0000-0002-9171-2569 |1 https://orcid.org/0000-0002-9171-2569 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Helix Structures in Quantum Cohomology of Fano Varieties |h [electronic resource] / |c by Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti. |
| 250 | |a 1st ed. 2024. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2024. | |
| 300 | |a 1 online resource (XIII, 236 p. 18 illus.). |b 15 illus. in color. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2356 | |
| 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Algebraic geometry. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 0 | |a Algebra, Homological. | |
| 650 | 1 | 4 | |a Algebraic Geometry. |
| 650 | 2 | 4 | |a Mathematical Physics. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Differential Geometry. |
| 650 | 2 | 4 | |a Category Theory, Homological Algebra. |
| 700 | 1 | |a Dubrovin, Boris A. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Guzzetti, Davide. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031690662 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031690686 |
| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2356 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-69067-9 |
| 912 | |a ZDB-2-SMA | ||
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||