P-Resolution Fans and Versal Component Dimension for Cyclic Quotient Singularities
نویسنده
چکیده
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.
منابع مشابه
Calculating 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 کاملP-Resolutions of Cyclic Quotients from the Toric Viewpoint
(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...
متن کاملOne-Parameter Toric Deformations of Cyclic Quotient Singularities
In the case of two-dimensional cyclic quotient singularities, we classify all oneparameter toric deformations in terms of certain Minkowski decompositions introduced by Altmann [1]. In particular, we describe to which components each such deformation maps, show how to induce each deformation from a versal family, give explicit equations for each deformation, describe the singularities in the ge...
متن کاملThe Versal Deformation of Cyclic Quotient Singularities
We describe the versal deformation of two-dimensional cyclic quotient singularities in terms of equations, following Arndt, Brohme and Hamm. For the reduced components the equations are determined by certain systems of dots in a triangle. The equations of the versal deformation itself are governed by a different combinatorial structure, involving rooted trees. One of the goals of singularity th...
متن کاملWild Quotient Singularities of Surfaces
Let (B,MB) denote a regular local ring of dimension two. Let H be a finite cyclic group acting on B, and let Z := Spec(B). Assume that the action of H on Spec(B) is free off the closed point, and thatMB is the only singular point of Z. Let f : X → Z be a resolution of the singularity, minimal with the property that the irreducible components of f(MB ) are smooth with normal crossings. Such a re...
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 2009