Stable maps in higher dimensions

Dervan, R. and Ross, J. (2019) Stable maps in higher dimensions. Mathematische Annalen, 374(3-4), pp. 1033-1073. (doi: 10.1007/s00208-018-1706-8)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dervan, Dr Ruadhaí
• Authors: Dervan, R., and Ross, J.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematische Annalen
• Publisher: Springer
• ISSN: 0025-5831
• ISSN (Online): 1432-1807
• Published Online: 13 June 2018
• Copyright Holders: Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2018
• First Published: First published in Mathematische Annalen 374(3-4):1033-1073
• Publisher Policy: Reproduced in accordance with the publisher copyright policy