| 000 | 03842nam a22006135i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-69067-9 | ||
| 003 | DE-He213 | ||
| 005 | 20251030113250.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 241029s2024 sz | s |||| 0|eng d | ||
| 020 |
_a9783031690679 _9978-3-031-69067-9 |
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| 024 | 7 |
_a10.1007/978-3-031-69067-9 _2doi |
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| 050 | 4 | _aQA564-609 | |
| 072 | 7 |
_aPBMW _2bicssc |
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| 072 | 7 |
_aMAT012010 _2bisacsh |
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| 072 | 7 |
_aPBMW _2thema |
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| 100 | 1 |
_aCotti, Giordano. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _986777 |
|
| 245 | 1 | 0 |
_aHelix Structures in Quantum Cohomology of Fano Varieties _h[electronic resource] / _cby Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti. |
| 250 | _a1st ed. 2024. | ||
| 264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Springer, _c2024. |
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| 300 |
_aXIII, 236 p. 18 illus., 15 illus. in color. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aLecture Notes in Mathematics, _x1617-9692 ; _v2356 |
|
| 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 | _aThis 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 | _aAlgebraic geometry. | |
| 650 | 0 | _aMathematical physics. | |
| 650 | 0 | _aDifferential equations. | |
| 650 | 0 |
_aGeometry, Differential. _969684 |
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| 650 | 0 |
_aAlgebra, Homological. _970150 |
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| 650 | 1 | 4 | _aAlgebraic Geometry. |
| 650 | 2 | 4 | _aMathematical Physics. |
| 650 | 2 | 4 | _aDifferential Equations. |
| 650 | 2 | 4 |
_aDifferential Geometry. _969686 |
| 650 | 2 | 4 |
_aCategory Theory, Homological Algebra. _970155 |
| 700 | 1 |
_aDubrovin, Boris A. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _986778 |
|
| 700 | 1 |
_aGuzzetti, Davide. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _986779 |
|
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031690662 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031690686 |
| 830 | 0 |
_aLecture Notes in Mathematics, _x1617-9692 ; _v2356 _975434 |
|
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-69067-9 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-SXMS | ||
| 912 | _aZDB-2-LNM | ||
| 999 |
_c64576 _d64576 |
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