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arXiv · 1708.09750

Stable maps in higher dimensions

Ruadhaí Dervan·Julius Ross
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Abstract

We formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-stability when the target is a point. We give some examples, such as Kodaira embeddings and fibrations. We prove the existence of a projective moduli space of canonically polarised stable maps, generalising the Kontsevich-Alexeev moduli space of stable maps in dimensions one and two. We also state an analogue of the Yau-Tian-Donaldson conjecture in this setting, relating stability of maps to the existence of certain canonical Kähler metrics.

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Ruadhaí Dervan, Julius Ross. 2018-05-30. Stable maps in higher dimensions. https://arxiv.org/abs/1708.09750

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