P-Resolutions of Cyclic Quotients from the Toric Viewpoint
نویسنده
چکیده
(1.1) The break through in deformation theory of (two-dimensional) quotient singularities Y was Kollár/Shepherd-Barron’s discovery of the one-to-one correspondence between so-called P-resolutions, on the one hand, and components of the versal base space, on the other hand (cf. [KS], Theorem (3.9)). It generalizes the fact that all deformations admitting a simultaneous (RDP-) resolution form one single component, the Artin component.
منابع مشابه
P-Resolution Fans and Versal Component Dimension for Cyclic Quotient Singularities
We use Altmann’s toric fan description of P-resolutions [Alt98] to calculate dimensions of the (reduced) versal base space components for two-dimensional cyclic quotient singularities.
متن کاملAzumaya Structure on D-branes and Deformations and Resolutions of a Conifold Revisited: Klebanov-strassler-witten vs. Polchinski-grothendieck
In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a conifold from the viewpoint of the Azumaya structure on D-branes and toric geometry. The details of how deformations and resolutions of the standard toric conifold Y can be obtained via morphisms from Azumaya points are...
متن کامل3-manifolds Admitting Toric Integrable Geodesic Flows
A toric integrable geodesic flow on a manifold M is a completely integrable geodesic flow such that the integrals generate a homogeneous torus action on the punctured cotangent bundle T ∗M \ M . A toric integrable manifold is a manifold which has a toric integrable geodesic flow. Toric integrable manifolds can be characterized as those whose cosphere bundle (the sphere bundle in the cotangent b...
متن کاملCalculating Milnor Numbers and Versal Component Dimensions from P-Resolution Fans
We use Altmann’s toric fan description of P-resolutions [Alt98] to formulate a new description of deformation theory invariants for two-dimensional cyclic quotient singularities. In particular, we show how to calculate the dimensions of the (reduced) versal base space components as well as Milnor numbers of smoothings over them.
متن کاملStability of Quiver Representations and Topology Change
We study phase structure of the moduli space of a D0-brane on the orbifold C3/Z2 × Z2 based on stability of quiver representations. It is known from an analysis using toric geometry that this model has multiple phases connected by flop transitions. By comparing the results of the two methods, we obtain a correspondence between quiver representations and geometry of toric resolutions of the orbi...
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 1996