Search results for "Gravitation"
showing 10 items of 743 documents
Cluster tilting for one-dimensional hypersurface singularities
2008
In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite dimensional symmetric and satisfy $\tau^2=\id$. In particular, we compute 2-CY tilted algebras for simple and minimally elliptic curve singularities.
On a Theorem of Greuel and Steenbrink
2017
A famous theorem of Greuel and Steenbrink states that the first Betti number of the Milnor fibre of a smoothing of a normal surface singularity vanishes. In this paper we prove a general theorem on the first Betti number of a smoothing that implies an analogous result for weakly normal singularities.
Stable Images and Discriminants
2020
We show that the discriminant/image of a stable perturbation of a germ of finite \(\mathcal {A}\)-codimension is a hypersurface with the homotopy type of a wedge of spheres in middle dimension, provided the target dimension does not exceed the source dimension by more than one. The number of spheres in the wedge is called the discriminant Milnor number/image Milnor number. We prove a lemma showing how to calculate this number, and show that when the target dimension does not exceed the source dimension, the discriminant Milnor number and the \(\mathcal {A}\)-codimension obey the “Milnor–Tjurina relation” familiar in the case of isolated hypersurface singularities. This relation remains conj…
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.
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.
Study of the Extended Narrow‐Line Region in the Host Galaxy of the Lensed QSO 2237+0305 (z= 1.69)
2004
The detection of spatially extended line emission in multiply imaged QSOs offers a new possibility to study the properties (kinematics and structure) of the ionized gas in the host galaxies of high-redshift QSOs. We have studied the arc of extended emission detected in Q2237+0305, finding that it arises from the core of the C III] λ1909 emission line and that the emission in the wings is compact. From the morphology of the emission-line profiles we have identified an additional narrow emission line component affecting the core of the spectra in the region of the arc (around component D). The kinematic analysis shows that the extended narrow-line region (NLR) exhibits broadening similar to t…
Microlensing of a Biconical Broad‐Line Region
2006
The influence of microlensing in the profiles of the emission lines generated in a biconical geometry is discussed. Microlensing amplification in this anisotropic model is not directly related to the bicone's intrinsic size but depends on the orientation of the bicone axis and on the cone aperture. The orientation of the projected bicone with respect to the shear of the magnification pattern can induce very interesting effects, like the quasi-periodic enhancements of the red/blue part of the emission line profile or the lack of correlation between the broad line region (BLR) and continuum light curves of QSOs. The emission line profiles of a BLR moving in a high caustic concentration exhibi…
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.