Beauville Surfaces and Groups by Ingrid Bauer, Shelly Garion, Alina Vdovina

By Ingrid Bauer, Shelly Garion, Alina Vdovina

This number of surveys and study articles explores a desirable category of types: Beauville surfaces. it's the first time that those items are mentioned from the issues of view of algebraic geometry in addition to team idea. The publication additionally comprises a number of open difficulties and conjectures with regards to those surfaces.

Beauville surfaces are a category of inflexible typical surfaces of common sort, which might be defined in a only algebraic combinatoric means. They play a massive function in numerous fields of arithmetic like algebraic geometry, team concept and quantity concept. The proposal of Beauville floor used to be brought by means of Fabrizio Catanese in 2000 and after the 1st systematic learn of those surfaces through Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there was an expanding curiosity within the subject.

These complaints replicate the themes of the lectures offered throughout the workshop ‘Beauville surfaces and teams 2012’, held at Newcastle collage, united kingdom in June 2012. This convention introduced jointly, for the 1st time, specialists of other fields of arithmetic drawn to Beauville surfaces.

Show description

Read Online or Download Beauville Surfaces and Groups PDF

Similar abstract books

Groebner bases and commutative algebra

The center-piece of Grobner foundation concept is the Buchberger set of rules, the significance of that is defined, because it spans mathematical idea and computational functions. This entire remedy comes in handy as a textual content and as a reference for mathematicians and laptop scientists and calls for no must haves except the mathematical adulthood of a sophisticated undergraduate.

Group Rings and Class Groups

The 1st a part of the publication facilities round the isomorphism challenge for finite teams; i. e. which houses of the finite staff G may be decided through the critical workforce ring ZZG ? The authors have attempted to give the consequences roughly selfcontained and in as a lot generality as attainable in regards to the ring of coefficients.

Finite Classical Groups [Lecture notes]

(London Taught direction heart 2013)

Extra info for Beauville Surfaces and Groups

Sample text

C. Bauer, F. Catanese, F. Grunewald, The classification of surfaces with pg = q = 0 isogenous to a product of curves. Pure Appl. Math. Q. 4(2), 547–586 (2008) Regular Algebraic Surfaces, Ramification Structures and Projective Planes 33 6. W. Bosma, J. Cannon, C. Playoust, The Magma algebra system. I. The user language. J. Symb. Comput. 24(3–4), 235–265 (1997) 7. H. Bruck, Quadratic extensions of cyclic planes, in Proceedings Symposium in Applied Mathematics, pp. 15–44 (1960) 8. I. M. Mantero, T.

The following array illustrates a basic projection λ: 0:1 1:3 2:4 3:0 4:1 5:0 6:0 4 2 3 4 5 2 1 2 5 6 5 6 6 3. Here, every point k represents a row and is followed by the points contained in the associated line λ(k). For example, the line λ(3) consists of the points 0, 4, 5. e. for (0, 1, 3) ∈ T we also have (1, 3, 0), (3, 0, 1) ∈ T . The associated group presentation G T agrees with the presentation of G 0 in (1). 9 [18, Example 2] The projective plane P of order 4 can be partitioned by three projective planes of order two (see [7]).

J. Algebra 340(1), 13–27 (2011) 10. J. Howie, On the SQ-universality of T (6)-groups. Forum Math. 1(3), 251–272 (1989) 11. A. O’Brien, The p-group generation algorithm. J. Symb. Comput. 9, 677–698 (1990) Strongly Real Beauville Groups Ben Fairbairn Abstract A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups.

Download PDF sample

Rated 4.01 of 5 – based on 38 votes