G.-M. Greuel, C. Hertling and G. Pfister, Moduli Spaces of Semiquasihomogeneous Singularities with fixed Principal Part. J. of Alg. Geom. 6, no. 1, 169--199 (1997).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....moduli space ( MuF] Ne] Classically, moduli spaces have been constructed for global algebraic objects such as projective varieties, or for vector bundles on a fixed projective variety. During the past years there has also been some progress in constructing moduli spaces for singularities (cf. [GHP]) and for Cohen Macaulay modules on a fixed local ring of a curve singularity ( GP3] see also [Gr1] for a survey) Indeed, the methods of proof are constructible and can be transferred to algorithms and finally to programmes. In the following, we describe an algorithm to compute a moduli space ....

....ring of a curve singularity ( GP3] see also [Gr1] for a survey) Indeed, the methods of proof are constructible and can be transferred to algorithms and finally to programmes. In the following, we describe an algorithm to compute a moduli space for isolated hypersurface singularities, following [GHP]. The algorithm has been developed and implemented in Singular by T. Bayer ( Ba] Let w = w 1 ; wn ) 2 Z n , w i 0, be a weight vector and f 2 C fx 1 ; xn g a semiquasihomogeneous power series, i.e. f = f 0 X hw;ffi d c ff x ff ; f 0 = X hw;ffi=d c ff x ff such ....

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G.-M. Greuel, C. Hertling and G. Pfister, Moduli Spaces of Semiquasihomogeneous Singularities with fixed Principal Part. J. of Alg. Geom. 6, no. 1, 169--199 (1997).

.... of finding sufficient and manageable conditions to guarantee that the geometric quotient X=G exists is of fundamental interest in the theory of moduli spaces for local objects such as isolated singularities or (Cohen Macaulay) modules over the local ring of a singularity (cf. L P] G P2] [G H P], H] In [G P1] we derived such conditions which are complemented in this paper. These conditions are even useful when the geometric quotient does not exist globally. Namely, they allow the construction of a stratification of X into locally closed G stable subschemes on which the geometric ....

....if the canonical map Spec A Gamma Spec A G is flat, then Spec A is mapped onto an open set U ae Spec A G such that Spec A i U is a geometric quotient and a principal fibre bundle with group G. This article was inspired by discussions with C. Hertling, when we tried to extend the results of [G H P], in order to construct moduli spaces for semiquasihomogeneous hypersurface singularities without fixing the principal part. We could not prove the existence of a geometric quotient as an algebraic C scheme. From the examples of Deveney and Finston we learned that, additionally, at least the ....

Greuel, G.-M.; Hertling, C.; Pfister, G.: Moduli spaces of semiquasihomogeneous singularities with fixed principal part. Preprint 264, University of Kaiserslautern, 1995. To be published in J. Algebraic Geometry.

.... of finding sufficient and manageable conditions to guarantee that the geometric quotient X=G exists is of fundamental interest in the theory of moduli spaces for local objects such as isolated singularities or (Cohen Macaulay) modules over the local ring of a singularity (cf. L P] G P2] [G H P], H] In [G P1] we derived such conditions which are complemented in this paper. These conditions are even useful when the geometric quotient does not exist globally. Namely, they allow construction of a stratification of X into locally closed G stable subschemes on which the geometric quotient ....

....if the canonical map Spec A Gamma S pec A G is flat, then SpecA is mapped onto an open set U ae Spec A G such that Spec A i U is a geometric quotient and a principal fibre bundle with group G. This article was inspired by discussions with C. Hertling, when we tried to extend the results of [G H P], in order to construct moduli spaces for semiquasihomogeneous hypersurface singularities without fixing the principal part. We could not prove the existence of a geometric quotient as an algebraic C scheme. From the examples of Deveney and Finston we learned that, additionally, at least the ....

Greuel, G.-M.; Hertling, C.; Pfister, G.: Moduli spaces of semiquasihomogeneous singularities with fixed principal part. Preprint 264, University of Kaiserslautern, 1995.

.... general it is merely a (connected) topological space (not even Hausdorff) In order to obtain a (coarse) moduli space as an algebraic variety, we have to stratify V h (S) into invariant strata and call the disjoint union of these strata, M(S) the moduli space of a topological singularity S (cf. [33]) What may be a good compactification of M(S) This may be important in view of Theorem 3 There is an open dense subset U ae V h (S) such that for any analytic singularity A 2 U there exists an irreducible curve of degree d 14 q (S) having one singular point of type A as its only ....

Greuel, G.-M. and Pfister G. On moduli spaces of semiquasihomogeneous singularities. Progress in mathematics 134, 171-185, Birkhauser 1996.

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Greuel, G.-M., Pfister, G., Hertling, C. Moduli spaces of semiquasihomogeneous singularities with fixed principal part. To be published in J. Algebraic Geometry.

No context found.

Greuel, G.M., Hertling, C., Pfister, G., Moduli Spaces of Semiquasihomogeneous Singularities with fixed Principal Part, Universitat Kaiserslautern, Preprint Nr. 264 (1995)

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