Contractions of 3-folds: deformations and invariants
Abstract
This note discusses recent new approaches to studying flopping curves on 3-folds. In a joint paper, the author and Michael Wemyss introduced a 3-fold invariant, the contraction algebra, which may be associated to such curves. It characterises their geometric and homological properties in a unified manner, using the theory of noncommutative deformations. Toda has now clarified the enumerative significance of the contraction algebra for flopping curves, calculating its dimension in terms of Gopakumar-Vafa invariants. Before reviewing these results, and others, I give a brief introduction to the rich geometry of flopping curves on 3-folds, starting from the resolutions of Kleinian surface singularities. This is based on a talk given at VBAC 2014 in Berlin.
Keywords
Cite
@article{arxiv.1511.01656,
title = {Contractions of 3-folds: deformations and invariants},
author = {Will Donovan},
journal= {arXiv preprint arXiv:1511.01656},
year = {2015}
}
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15 pages