Skew configurations of lines in real del pezzo surfaces

Zabun, Remziye Arzu
By blowing up projective plane at n<9 points which form a generic configuration, we obtain a del Pezzo surface X of degree d=9-n with a configuration of n skew lines that are exceptional curves over the blown-up points. The anti-canonical linear system maps X to a projective space of dimension d, P^{d}, and the images of these exceptional curves form a configuration of n lines in P^{d}. The subject of our research is the correspondence between the configurations of n generic points in a real projective plane, RP^{2}, and the configurations of n lines in a (9-n)-dimensional real projective space, i.e. RP^{9-n}. This correspondence is nontrivial in the cases n=6 and n=7. We study the correspondence between on such generic configurations of n points in RP^{2} and such configurations of lines in RP^{9-n}. In the case of n=6, there exist precisely 4 deformation classes of generic planar configurations of 6 points, and we describe the corresponding 4 deformation classes of configurations of 6 skew lines in RP^{3}. In the case n=7, there exist precisely 14 deformation classes of generic planar configurations of 7 points and we describe the corresponding 14 deformation classes of configurations of 7 bitangents to a quartic curve (such configurations are known in the literature as Aronhold sets).


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Static, spherically symmetric solutions of axidilaton gravity in D dimensions are given in the Brans-Dicke frame for arbitrary values of the Brans-Dicke constant omega and an axion-dilaton coupling parameter k. The mass and the dilaton and axion charges are determined and a BPS bound is derived. There exists a one-parameter family of black hole solutions in the scale-invariant limit.
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A finite rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map defined on this subcomplex into the curve complex is induced from an automorphism of curve complex. In this thesisi we find finite rigid sets in the curve complexes of connected, non-orientable surfaces of genus g with n holes, where g+n neq 4. 
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Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28)
We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
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CP1 sigma model with Hopf interaction in 1 + 2 dimensions is quantized canonically using a lifted formulation. In this formulation the Hopf invariant is still a local functional of the fields. However, the constraint structure is as simple as that of a U(1) gauge theory without any nonlinearity constraints. As a by-product, the theta-dependent fractional spin is computed in this local setting.
ERIS, A; GURSES, M; Karasu, Atalay (AIP Publishing, 1984-01-01)
We formulate stationary axially symmetric (SAS) Einstein–Maxwell fields in the framework of harmonic mappings of Riemannian manifolds and show that the configuration space of the fields is a symmetric space. This result enables us to embed the configuration space into an eight‐dimensional flat manifold and formulate SAS Einstein–Maxwell fields as a σ‐model. We then give, in a coordinate free way, a Belinskii–Zakharov type of an inverse scattering transform technique for the field equations supplemented by a...
Citation Formats
R. A. Zabun, “Skew configurations of lines in real del pezzo surfaces,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.