On a series of Gorenstein cyclic quotient singularities admitting a unique projective crepant resolution
| dc.creator | Dais, Dimitrios I. | |
| dc.creator | Henk, Martin | |
| dc.date | 1998-03-20 | |
| dc.date.accessioned | 2026-07-07T05:24:08Z | |
| dc.date.available | 2026-07-07T05:24:08Z | |
| dc.description | In this paper we prove that the Gorenstein cyclic quotient singularities of type \frac 1l (1,..., 1,l-(r-1)) with $l\geq r\geq 2$, have a \textit{unique}torus-equivariant projective, crepant, partial resolution, which is ``full'' iff either $l\equiv 0$ mod $% (r-1) $ or $l\equiv 1$ mod $(r-1) $. As it turns out, if one of these two conditions is fulfilled, then the exceptional locus of the full desingularization consists of $\lfloor \frac{l}{r-1} \rfloor$ prime divisors, $\lfloor \frac{l}{r-1}\rfloor - 1$ of which are isomorphic to the total spaces of $\Bbb{P}_{\Bbb{C}}^1$-bundles over $\Bbb{P}_{\Bbb{C}%}^{r-2}$. Moreover, it is shown that intersection numbers are computable explicitly and that the resolution morphism can be viewed as a composite of successive (normalized) blow-ups. Obviously, the monoparametrized singularity-series of the above type contains (as its ``first member'') the well-known Gorenstein singularity defined by the origin of the affine cone which lies over the $r$-tuple Veronese embedding of $\Bbb{P}_{\Bbb{C}}^{r-1}$. | |
| dc.description | 96 pages. 14 Figures. LaTeX 2e with AMS and epsfig macros. This is the revised version of the ZIB preprint SC-97-39. To appear in the DMV-Seminar-Volume "Combinatorial Convex Geometry and Toric Varieties", Birkhaeuser. (For correct placement of figures we would recommend the use of the LaTeX sources instead of the direct PostScript link) | |
| dc.identifier | https://arxiv.org/abs/math/9803094 | |
| dc.identifier | http://arxiv.org/abs/math/9803094 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76723 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M25, 14Q15 | |
| dc.title | On a series of Gorenstein cyclic quotient singularities admitting a unique projective crepant resolution | |
| dc.type | text |