Abstract
In this last chapter we turn to the analysis of important developments in complex geometry which took place in the 1980–1990s, directly motivated by supersymmetry and supergravity and completely inconceivable outside such a framework. Notwithstanding their roots in the theoretical physics of the superworld, such developments constitute, by now, the basis of some of the most innovative and alive research directions of contemporary geometry.
Quando chel cubo con le cose appresso
Se agguaglia a qualche numero discreto
Trouan dui altri differenti in esso.
Niccoló Tartaglia
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Notes
- 1.
- 2.
This result was derived in private conversations of the author with Dimitry Markushevich.
- 3.
A resolution of singularities \(X \rightarrow Y\) is crepant when the canonical bundle of X is the pullback of the canonical bundle of Y.
- 4.
A variety is Gorenstein when the canonical divisor is a Cartier divisor, i.e., a divisor corresponding to a line bundle.
- 5.
Following standard mathematical nomenclature, we call compatible connection on a holomorphic vector bundle, one whose (0, 1) part is the Cauchy Riemann operator of the bundle.
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Fré, P.G. (2018). (Hyper)Kähler Quotients, ALE-Manifolds and \(\mathbb {C}^n/\varGamma \) Singularities. In: Advances in Geometry and Lie Algebras from Supergravity. Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-74491-9_8
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