489 research outputs found
Polygonal valuations
AbstractWe develop a valuation theory for generalized polygons similar to the existing theory for dense near polygons. This valuation theory has applications for the study and classification of generalized polygons that have full subpolygons as subgeometries
Modal logic of planar polygons
We study the modal logic of the closure algebra , generated by the set
of all polygons in the Euclidean plane . We show that this logic
is finitely axiomatizable, is complete with respect to the class of frames we
call "crown" frames, is not first order definable, does not have the Craig
interpolation property, and its validity problem is PSPACE-complete
Decomposition in bunches of the critical locus of a quasi-ordinary map
A polar hypersurface P of a complex analytic hypersurface germ, f=0, can be
investigated by analyzing the invariance of certain Newton polyhedra associated
to the image of P, with respect to suitable coordinates, by certain morphisms
appropriately associated to f. We develop this general principle of Teissier
(see Varietes polaires. I. Invariants polaires des singularites
d'hypersurfaces, Invent. Math. 40 (1977), 3, 267-292) when f=0 is a
quasi-ordinary hypersurface germ and P is the polar hypersurface associated to
any quasi-ordinary projection of f=0. We build a decomposition of P in bunches
of branches which characterizes the embedded topological type of the
irreducible components of f=0. This decomposition is characterized also by some
properties of the strict transform of P by the toric embedded resolution of f=0
given by the second author in a paper which will appear in Annal. Inst. Fourier
(Grenoble). In the plane curve case this result provides a simple algebraic
proof of the main theorem of Le, Michel and Weber in "Sur le comportement des
polaires associees aux germes de courbes planes", Compositio Math, 72, (1989),
1, 87-113
Freeform User Interfaces for Graphical Computing
報告番号: 甲15222 ; 学位授与年月日: 2000-03-29 ; 学位の種別: 課程博士 ; 学位の種類: 博士(工学) ; 学位記番号: 博工第4717号 ; 研究科・専攻: 工学系研究科情報工学専
On the Galois group of Generalized Laguerre Polynomials
Using the theory of Newton Polygons, we formulate a simple criterion for the
Galois group of a polynomial to be ``large.'' For a fixed \alpha \in \Q -
\Z_{<0}, Filaseta and Lam have shown that the th degree Generalized
Laguerre Polynomial is irreducible for all large enough . We use
our criterion to show that, under these conditions, the Galois group of \La
is either the alternating or symmetric group on letters, generalizing
results of Schur for .Comment: 6 page
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