Search results for "Singularity"
showing 10 items of 352 documents
Flat lightlike hypersurfaces in Lorentz–Minkowski 4-space
2009
Abstract The lightlike hypersurfaces in Lorentz–Minkowski space are of special interest in Relativity Theory. In particular, the singularities of these hypersurfaces provide good models for the study of different horizon types. We introduce the notion of flatness for these hypersurfaces and study their singularities. The classification result asserts that a generic classification of flat lightlike hypersurfaces is quite different from that of generic lightlike hypersurfaces.
Families of ICIS with constant total Milnor number
2021
We show that a family of isolated complete intersection singularities (ICIS) with constant total Milnor number has no coalescence of singularities. This extends a well-known result of Gabriélov, Lazzeri and Lê for hypersurfaces. We use A’Campo’s theorem to see that the Lefschetz number of the generic monodromy of the ICIS is zero when the ICIS is singular. We give a pair applications for families of functions on ICIS which extend also some known results for functions on a smooth variety.
Logarithmic Vector Fields and the Severi Strata in the Discriminant
2017
The discriminant, D, in the base of a miniversal deformation of an irreducible plane curve singularity, is partitioned according to the genus of the (singular) fibre, or, equivalently, by the sum of the delta invariants of the singular points of the fibre. The members of the partition are known as the Severi strata. The smallest is the δ-constant stratum, D(δ), where the genus of the fibre is 0. It is well known, by work of Givental’ and Varchenko, to be Lagrangian with respect to the symplectic form Ω obtained by pulling back the intersection form on the cohomology of the fibre via the period mapping. We show that the remaining Severi strata are also co-isotropic with respect to Ω, and mor…
Invariants of unipotent groups
1987
I’ll give a survey on the known results on finite generation of invariants for nonreductive groups, and some conjectures. You know that Hilbert’s 14th problem is solved for the invariants of reductive groups; see [12] for a survey. So the general case reduces to the case of unipotent groups. But in this case there are only a few results, some negative and some positive. I assume that k is an infinite field, say the complex numbers, but in most instances an arbitrary ring would do it.
A Property on Singularities of NURBS Curves
2002
We prove that if a.n open Non Uniform Rational B-Spline curve of order k has a singular point, then it belongs to both curves of order k - 1 defined in the k - 2 step of the de Boor algorithm. Moreover, both curves are tangent at the singular point.
Illustrating the classification of real cubic surfaces
2006
Knorrer and Miller classified the real projective cubic surfaces in P(R) with respect to their topological type. For each of their 45 types containing only rational double points we give an affine equation, s.t. none of the singularities and none of the lines are at infinity. These equations were found using classical methods together with our new visualization tool surfex. This tool also enables us to give one image for each of the topological types showing all the singularities and lines.
Bifurcation of Singularities Near Reversible Systems
1994
In this paper we study generic unfoldings of certain singularities in the class of all C ∞ reversible systems on R 2.
Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
2020
We consider Feynman integrals with algebraic leading singularities and total differentials in $\epsilon\,\mathrm{d}\ln$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable roots in terms of conventional multiple polylogarithms, by either parametric integration or matching the symbol. As our main application, we evaluate the two-loop master integrals relevant to the $\alpha \alpha_s$ corrections to Drell-Yan lepton pair production at hadron colliders. We optimize our functional basis to allow for fast and stable numerical evaluations in the physical region of phase space.
A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes
2010
We show that a well-known simple formula for the explicit infrared poles of one-loop QCD amplitudes has a corresponding simple counterpart in unintegrated form. The unintegrated formula approximates the integrand of one-loop QCD amplitudes in all soft and collinear singular regions. It thus defines a local counter-term for the infrared singularities and can be used as an ingredient for the numerical calculation of one-loop amplitudes.
Infrared Singularities and Soft Gluon Resummation with Massive Partons
2010
Infrared divergences of QCD scattering amplitudes can be derived from an anomalous dimension matrix, which is also an essential ingredient for the resummation of large logarithms due to soft gluon emissions. We report a recent analytical calculation of the anomalous dimension matrix with both massless and massive partons at two-loop level, which describes the two-loop infrared singularities of any scattering amplitudes with an arbitrary number of massless and massive partons, and also enables soft gluon resummation at next-to-next-to-leading-logarithmic order. As an application, we calculate the infrared poles in the q qbar -> t tbar and gg -> t tbar scattering amplitudes at two-loop …