Cremona groups and the icosahedron / Ivan Cheltsov and Constantin Shramov.
Material type:
TextSeries: Monographs and research notes in mathematicsPublication details: Boca Raton : CRC Press, ©2016.Description: xxi, 504 pages : illustrations ; 24 cmISBN: - 9781482251593
- 516.35 23 C516
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 516.35 C516 (Browse shelf(Opens below)) | Available | 137449 |
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| 516.35 C397(85-3) Theory of moduli | 516.35 C397(91/2) Arithmetic algebraic geometry | 516.35 C397(93/2) Algebraic cycles and Hodge theory | 516.35 C516 Cremona groups and the icosahedron / | 516.35 C621 Arithmetic geometry | 516.35 C621 Arithmetic geometry : | 516.35 C714 Symplectic geometry |
Includes bibliographical references and index.
1. Introduction --
I. Preliminaries --
2. Singularities of pairs --
3. Noether - Fano inequalities --
4. Auxiliary results --
II. Icosahedral group --
5. Basic properties --
6. Surfaces with icosahedral symmetry --
III. Quintic del Pezzo threefold --
7. Quintic del Pezzo threefold --
8. Anticanonical linear system --
9. Combinatorics of lines and conics --
10. Special invariant curves --
11. Two Sarkisov links --
IV. Invariant subvarieties --
12. Invariant cubic hypersurface --
13. Curves of low degree --
14. Orbits of small length --
15. Further properties of the invariant cubic --
16. Summary of orbits, curves, and surfaces --
V. Singularities of linear systems --
17. Base loci of invariant linear systems --
18. Proof of the main result --
19. Halphen pencils and elliptic fibrations.
The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity. It presents up-to-date tools for studying birational geometry of higher-dimensional varieties. In particular, it provides readers with a deep understanding of the biregular and birational geometry of V5.
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