Displaying similar documents to “GIT quotients of products of projective planes”

Differential equations on the plane with given solutions.

R. Ramírez, N. Sadovskaia (1996)

Collectanea Mathematica

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The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

Stoichev, Stoicho (2007)

Serdica Journal of Computing

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The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006. Two heuristic algorithms (M65 and M52) for finding respectively unitals and maximal arcs in projective planes of order 16 are described. The exact algorithms based on exhaustive search are impractical because of the combinatorial explosion (huge number of combinations to be checked). Algorithms M65 and...

Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups

Jean-Marc Drézet, Günther Trautmann (2003)

Annales de l’institut Fourier

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We extend the methods of geometric invariant theory to actions of non–reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non–reductive. Given a linearization of the natural action of the group Aut ( E ) × Aut ( F ) on Hom(E,F), a homomorphism is called stable if its orbit with respect to the unipotent radical is contained in the stable locus with respect to the natural reductive subgroup of the automorphism group. We encounter effective numerical conditions...

Non-free two-generator subgroups of SL(Q).

S. Peter Farbman (1995)

Publicacions Matemàtiques

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The question of whether two parabolic elements A, B of SL(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| < 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL(C) will not be free.

The number of conics tangent to five given conics: the real case.

Felice Ronga, Alberto Tognoli, Thierry Vust (1997)

Revista Matemática de la Universidad Complutense de Madrid

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It is a classical result, first established by de Jonquières (1859), that generically the number of conics tangent to 5 given conics in the complex projective plane is 3264. We show here the existence of configurations of 5 real conics such that the number of real conics tangent to them is 3264.