Jet schemes of rational double point singularities. (English) Zbl 1312.14047
Campillo, Antonio (ed.) et al., Valuation theory in interaction. Proceedings of the 2nd international conference and workshop on valuation theory, Segovia and El Escorial, Spain, July 18–29, 2011. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-149-1/hbk). EMS Series of Congress Reports, 373-388 (2014).
Summary: We prove that for \(m\in\mathbb{N}\), \(m\) large enough, the number of irreducible components of the schemes of \(m\)-jets centered at a point which is a double point singularity is independent of m and is equal to the number of exceptional curves on the minimal resolution of the singularity. We also relate some irreducible components of the jet schemes of an E6 singularity to its “minimal” embedded resolutions of singularities.
For the entire collection see [Zbl 1296.00049].
For the entire collection see [Zbl 1296.00049].
MSC:
| 14E18 | Arcs and motivic integration |
| 14B05 | Singularities in algebraic geometry |
| 13D40 | Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series |
