Cremona groups and the icosahedron. (2015)

• Record Type: Book
• Further Information: Note: Ivan Cheltsov, Constantin Shramov.
• Authors: Cheltsov, Ivan; Shramov, Constantin
• Contents: Introduction; Conjugacy in Cremona groups; Three-dimensional projective space; Other rational Fano threefolds; Statement of the main result; Outline of the book Preliminaries; Singularities of pairs ; Canonical and log canonical singularities; Log pairs with mobile boundaries; Multiplier ideal sheaves; Centers of log canonical singularities; Corti’s inequality Noether–Fano inequalities ; Birational rigidity; Fano varieties and elliptic fibrations; Applications to birational rigidity; Halphen pencils Auxiliary results; Zero-dimensional subschemes; Atiyah flops; One-dimensional linear systems; Miscellanea Icosahedral Group; Basic properties ; Action on points and curves; Representation theory; Invariant theory; Curves of low genera; SL2 (C) and PSL2 (C); Binary icosahedral group; Symmetric group; Dihedral group Surfaces with icosahedral symmetry ; Projective plane; Quintic del Pezzo surface; Clebsch cubic surface; Two-dimensional quadric; Hirzebruch surfaces; Icosahedral subgroups of Cr2 (C); K 3 surfaces Quintic del Pezzo Threefold ; Quintic del Pezzo threefold; Construction and basic properties; PSL2 (C)-invariant anticanonical surface; Small orbits; Lines; Orbit of length five; Five hyperplane sections; Projection from a line; Conics Anticanonical linear system ; Invariant anticanonical surfaces; Singularities of invariant anticanonical surfaces; Curves in invariant anticanonical surfaces Combinatorics of lines and conics ; Lines; Conics Special invariant curves ; Irreducible curves; Preliminary classification of low degree curves Two Sarkisov links ; Anticanonical divisors through the curve L6 ; Rational map to P4 ; A remarkable sextic curve; Two Sarkisov links; Action on the Picard group Invariant Subvarieties ; Invariant cubic hypersurface; Linear system of cubics; Curves in the invariant cubic; Bring’s curve in the invariant cubic; Intersecting invariant quadrics and cubic; A remarkable rational surface Curves of low degree; Curves of degree 16; Six twisted cubics; Irreducible curves of degree 18; A singular curve of degree 18; Bring’s curve; Classification Orbits of small length ; Orbits of length 20; Ten conics; Orbits of length 30; Fifteen twisted cubics Further properties of the invariant cubic ; Intersections with low degree curves; Singularities of the invariant cubic; Projection to Clebsch cubic surface; Picard group Summary of orbits, curves, and surfaces ; Orbits vs. curves; Orbits vs. surfaces; Curves vs. surfaces; Curves vs. curves Singularities of Linear Systems ; Base loci of invariant linear systems ; Orbits of length 10; Linear system Q3 ; Isolation of orbits in S; Isolation of arbitrary orbits; Isolation of the curve L15 Proof of the main result ; Singularities of linear systems; Restricting divisors to invariant quadrics; Exclusion of points and curves different from L15 ; Exclusion of the curve L15 ; Alternative approach to exclusion of points; Alternative approach to the exclusion of L15 Halphen pencils and elliptic fibrations ; Statement of results; Exclusion of points; Exclusion of curves; Description of non-terminal pairs; Completing the proof
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 516.1; Cremona transformations; Icosahedra
• Languages: English
• ISBNs: 9781482251609
• Related ISBNs: 9781482251593
• Notes: Note: Description based on CIP data; item not viewed.
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