Deformation classification of typical configurations of 7 points in the real projective plane

A configuration of 7 points in RP2 is called typical if it has no collinear triples and no coconic sextuples of points. We show that there exist 14 deformation classes of such configurations. This yields classification of real Aronhold sets.


Geometric measures of entanglement
UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01)
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Inequalities for harmonic functions on spheroids and their applications
Zahariuta, V (2001-06-01)
Hadamard-type interpolational inequalities for norms of harmonic functions are studied for confocal prolate and oblate spheroids. It is shown that the optimal level domains in such inequalities may be non-spheroidal. Moreover, in contrary with the case of analytic functions, there is an unremovable gap between the corresponding optimal level domains for inner and outer versions of Hadamard-type inequalities for harmonic functions. These results are based on some special asymptotical formulas for associated ...
Skew configurations of lines in real del pezzo surfaces
Zabun, Remziye Arzu; Finashin, Sergey; Department of Mathematics (2014)
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 plan...
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential
AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01)
Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
Topology change for fuzzy physics: Fuzzy spaces as Hopf algebras
BALACHANDRAN, AP; Kürkcüoğlu, Seçkin (World Scientific Pub Co Pte Lt, 2004-08-10)
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S-2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field theories and modeling space-times by noncommutative manifolds. We show that fuzzy spaces are Hopf algebras and in fact have more structure than the latter. They are thus candidates for quantum symmetries. Using their generalized Hopf algebraic structures, we can also model proc...
Citation Formats
S. Finashin, “Deformation classification of typical configurations of 7 points in the real projective plane,” TOPOLOGY AND ITS APPLICATIONS, pp. 358–385, 2015, Accessed: 00, 2020. [Online]. Available: