Stable Maps in Higher Dimensions
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Dervan, R
Ross, Julius
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
Description
Keywords
4902 Mathematical Physics, 4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Mathematische Annalen
Conference Name
Journal ISSN
1432-1807
1432-1807
1432-1807
Volume Title
372
Publisher
Springer Nature
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/J002062/1)