Resolving Singularities with Cartan’s Prolongation
نویسندگان
چکیده
منابع مشابه
Understanding Singularities in Cartan's and Nsf Geometric Structures
In this work we establish a relationship between Cartan’s geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.
متن کاملVariational Approach to Differential Invariants of Rank 2 Vector Distributions
In the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n = 5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant fourth-order tensor invariant for such distributions, using his ”reduction-prolongation” procedure (see [12]). After Cartan’s work the following questions remained op...
متن کاملCartan’s structural equations for singular manifolds
The classical Cartan’s structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of singularities, we need to study the geometry of manifolds endowed on the tangent bundle with a symmetric bilinear form which is allowed to become degenerate. B...
متن کاملResolving 3-dimensional toric singularities
This paper surveys, in the first place, some basic facts from the classification theory of normal complex singularities, including details for the low dimensions 2 and 3. Next, it describes how the toric singularities are located within the class of rational singularities, and recalls their main properties. Finally, it focuses, in particular, on a toric version of Reid’s desingularization strat...
متن کاملResolving Singularities in (0,2) Models
In contrast to the familiar (2, 2) case, the singularities which arise in the (0, 2) setting can be associated with degeneration of the base Calabi–Yau manifold and/or with degenerations of the gauge bundle. We study a variety of such singularities and give a procedure for resolving those which can be cured perturbatively. Among the novel features which emerge are models in which smoothing sing...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008