Download e-book for iPad: Cremona groups and the icosahedron by Ivan Cheltsov, Constantin Shramov

By Ivan Cheltsov, Constantin Shramov

ISBN-10: 1482251604

ISBN-13: 9781482251609

ISBN-10: 4134154154

ISBN-13: 9784134154150

Cremona teams and the Icosahedron makes a speciality of the Cremona teams of ranks 2 and three and describes the attractive appearances of the icosahedral team A5 in them. The ebook surveys identified proof approximately surfaces with an motion of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and offers an evidence of its A5-birational rigidity.

The authors explicitly describe many fascinating A5-invariant subvarieties of V5, together with A5-orbits, low-degree curves, invariant anticanonical K3 surfaces, and a mildly singular floor of common style that may be a measure 5 conceal of the diagonal Clebsch cubic floor. additionally they current birational selfmaps of V5 that shuttle with A5-action and use them to figure out the total team of A5-birational automorphisms. due to this examine, they produce 3 non-conjugate icosahedral subgroups within the Cremona workforce of rank three, one in every of them bobbing up from the threefold V5.

This booklet offers updated instruments for learning birational geometry of higher-dimensional types. particularly, it presents readers with a deep knowing of the biregular and birational geometry of V5.

Show description

Read Online or Download Cremona groups and the icosahedron PDF

Best research books

Research Methods in Urban and Regional Planning by Dr. Xinhao Wang, Dr. Rainer vom Hofe (auth.) PDF

A part of the hot Tsinghua college Texts sequence, this ebook offers an updated advent to the elemental equipment on the topic of making plans and human prone supply. those tools reduction planners in answering the next the most important questions on human actions inside a given group: "Who are they?

Download e-book for kindle: Research Methods in Neurochemistry: Volume 5 by George H. DeVries (auth.), Neville Marks, Richard Rodnight

This 5th quantity of study tools in Neurochemistry represents a milestone in that it marks nearly a decade because the inception of the sequence. Over those ten years there was a virtually exponential progress in neuro­ chemistry observed by way of a variety of technical advancements. this can be the justification for our sequence; necessarily we now have in simple terms been capable of conceal a frac­ tion of the methodological thoughts of the decade, yet we have now attempted up to attainable to create a stability among different ways and philosophies within the research of the chemical foundation of mind functionality.

New PDF release: Die Psychologie der religiösen Mystik

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer publication files mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen.

Additional resources for Cremona groups and the icosahedron

Sample text

After this it is often possible to exclude most possibilities by considering some explicit intersections. In Chapter 17 we prove auxiliary facts about base loci of various A5 -invariant linear systems that will be used later in the process of isolation of centers of bad singularities. 1 we show that the points of A5 -orbits of length 10 in V5 are in some sense in sufficiently general position. 2 we use this information to determine the base locus of the unique two-dimensional A5 -invariant subsystem of the anticanonical linear system on V5 , which helps to isolate several A5 -orbits of small length.

In particular, it appears that many such curves are contained in the surfaces of the pencil Q2 . This allows us to demonstrate that there is only a finite number of A5 -invariant curves of degree less than 30 and justifies our further attempts to obtain a classification of invariant curves of low degree. In Chapter 9 we describe combinatorial properties of A5 -invariant curves in V5 that are unions of small numbers of lines or conics. In particular, we show that some of them are disjoint unions of lines or conics, and describe intersections in several other situations.

Moreover, for every ample Q-Cartier Q-divisor ∆ on X, there exists an effective Q-divisor BZ on the variety Z such that KX + BX + ∆ Z ∼Q KZ + BZ , and the log pair (Z, BZ ) has Kawamata log terminal singularities. Suppose, in addition, that X is faithfully acted on by a finite group G such that the boundary BX is G-invariant. Note that this does not mean that each Bi is G-invariant or that each Mj is G-invariant, since the group G can permute the divisors B1 , . . , Br and it can permute the linear systems M1 , .

Download PDF sample

Cremona groups and the icosahedron by Ivan Cheltsov, Constantin Shramov

by Ronald

Rated 4.83 of 5 – based on 31 votes