TY  - BOOK
AU  - Cheltsov,Ivan
AU  - Shramov,Constantin
TI  - Cremona groups and the icosahedron
T2  - Monographs and research notes in mathematics
SN  - 9781482251593 
U1  - 516.35 23
PY  - 2016///
CY  - Boca Raton : 
PB  - CRC Press, 
KW  - Algebraic geometry
KW  - Automorphic forms
N1  - 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
N2  - 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
ER  -