Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Torsion differentials and deformation


Author: D. S. Rim
Journal: Trans. Amer. Math. Soc. 169 (1972), 257-278
MSC: Primary 14B10; Secondary 14D15, 14M10
MathSciNet review: 0342513
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ S$-scheme $ X$ be a Schlessinger deformation of a curve $ {X_0}$ defined over a field $ k$. In §§1 and 2, the dimension of the parameter space $ S$, the relative differentials of $ X$ over $ S$, and the fibres with singularity were studied, in case when $ {X_0}$ is locally complete-intersection. In §3 we show that if $ k$-scheme $ {X_0}$ is a specialization of a smooth $ k$-scheme, then the punctured spectrum $ \operatorname{Spex} ({O_{{X_{0,x}}}})$ has to be connected for every point $ x \in {X_0}$ such that $ \dim {O_{{X_{0,x}}}} \geqslant 2$. In turn we construct a rigid singularity on a surface. In the last section a few conjectures amplifying those of P. Deligne are made.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14B10, 14D15, 14M10

Retrieve articles in all journals with MSC: 14B10, 14D15, 14M10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0342513-4
PII: S 0002-9947(1972)0342513-4
Article copyright: © Copyright 1972 American Mathematical Society