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Cremona groups and the icosahedron / Ivan Cheltsov and Constantin Shramov.

By: Contributor(s): Material type: TextTextSeries: Monographs and research notes in mathematicsPublication details: Boca Raton : CRC Press, ©2016.Description: xxi, 504 pages : illustrations ; 24 cmISBN:
  • 9781482251593
Subject(s): DDC classification:
  • 516.35 23 C516
Contents:
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.
Summary: 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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Holdings
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
Total holds: 0

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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