Equations defining rational singularities

Wahl, Jonathan

doi:10.24033/asens.1326

Cited by 68 publications

(37 citation statements)

References 13 publications

(27 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is in accordance with (and proved by) Ward's theorem on equations defining rational singularities [6].…”

supporting

confidence: 90%

Dihedral singularities: invariants, equations and infinitesimal deformations

Riemenschneider¹

1976

Bull. Amer. Math. Soc.

View full text Add to dashboard Cite

In this note we give a short survey on joint work with K. Behnke; details will appear in [1] and [2].Let n, q be positive integers with 2 < q < n and gcd(«, q) = l, m = n -q. We define elements 0 W , \jj , r\ E. GL( G n has finite order Amq\ G +1 is the binary dihedral group of order 4g. G w acts on C 2 in the usual way; the quotient C 2 /G n has precisely one (normal) complex-analytic singularity. We call it the dihedral singularity of type D n . If we expand n/q into the modified continued fraction à la HirzebruchJung,

show abstract

“…This is in accordance with (and proved by) Ward's theorem on equations defining rational singularities [6].…”

supporting

confidence: 90%

Dihedral singularities: invariants, equations and infinitesimal deformations

Riemenschneider¹

1976

Bull. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…In the proof of Theorem (5.4), we shall construct a syzygy of the Rees algebra of the singularity, which has a self-dual property in the T. N. -isomorphy sense. This is done by the following Wahl-Sally's method for "the lifting of the syzygy from the tangent cone to the original local ring [47], [40]". Their method is essential in our proof of Theorem (5.4).…”

Section: Proposition (48) Let (V P) Be a Normal Two-dimensional Gomentioning

confidence: 99%

“…(5.7) In this paragraph, we shall prove (5.6.3) under the assumption W 0 =U for i = l. We denote W 0 by Z and its strict transform by Zj as usual. To construct the desired isomorphism, we use the following: Lemma (5.7.1) (Artin-Rees-Wahl, Lemma i.6 [47] 2), we obtain the complex of graded S-modules…”

Section: Let G Be the Divisor On 17 Y Of The Form G= X (A S + R-s^)mentioning

confidence: 99%

A $p_g$-Formula and Elliptic Singularities

Tomari¹

1985

Publ. Res. Inst. Math. Sci.

View full text Add to dashboard Cite

“…It is not surprising that a few singularities besides quotient singularities might be semistable. Every rational singularity is the quotient of a Gorenstein singularity under the action of a cyclic group [19]. Thus, it is possible that cyclic quotients of some semistable elliptic singularities are semistable.…”

Section: Theorem 2 Suppose E=p Then (A) Grr Os Cohen-macaulay Anmentioning

confidence: 99%

“…The ideal I is generated by the 2 x2 minors of a 2 x 3 matrix M over A such that each generator is of order 2 in A [5,19]:…”

Section: Two-dimensional Triple Points Of Embedding Dimensionmentioning

confidence: 99%