On infinitesimal deformations and obstructions for rational surface singularities

Authors
Christophersen, JA Gustavsen, TS
Citation
Ja. Christophersen et Ts. Gustavsen, On infinitesimal deformations and obstructions for rational surface singularities, J ALGEBR GE, 10(1), 2001, pp. 179-198
Citations number
20
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF ALGEBRAIC GEOMETRY
ISSN journal
10563911 → ACNP
Volume
10
Issue
1
Year of publication
2001
Pages
179 - 198
Database
ISI
SICI code
1056-3911(200101)10:1<179:OIDAOF>2.0.ZU;2-8
Abstract
We prove dimension formulas for the cotangent spaces T-1 and T-2 that are v alid for all rational surface singularities X. The terms in the formulas in volve the multiplicity of X, the dimensions of the T-i for singularities on the blow-up of X and an invariant c(X) defined on the blow-up. We show tha t c(X) = 0 if the fundamental cycle is reduced, reproving a result of de Jo ng and van Straten.