On a remark by Y. Namikawa
Michele Rossi
TL;DR
This paper constructs examples to support Namikawa's conclusions and offers a geometric interpretation of the rigidity of certain rational curve configurations via factorization of small resolutions.
Contribution
It provides new examples confirming Namikawa's remarks and offers a geometric perspective on the rigidity properties of trees of rational curves.
Findings
Examples supporting Namikawa's conclusion
Geometric interpretation of rigidity properties
Factorization of small resolutions through nodal threefolds
Abstract
The aim of the present paper is on the one hand to produce examples supporting the conclusion of Y. Namikawa in Remark 2.8 of \cite{N} and improving considerations of Example 1.11 of the same paper. On the other hand, it is intended to give a geometric interpretation of the rigidity properties of some trees of exceptional rational curves, as observed by Namikawa, which can be obtained by factorizing small resolutions through nodal threefolds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Topics in Algebra · Mathematics and Applications