An exceptional locus in the perfect compactification of $A_g$
N. Shepherd-Barron
TL;DR
This paper investigates the properties of a specific line bundle on the perfect compactification of the moduli space of abelian varieties, showing its semi-ampleness in positive characteristic and identifying its exceptional locus.
Contribution
It proves the semi-ampleness of the line bundle 12M-D in positive characteristic and characterizes its exceptional locus across all characteristics.
Findings
Line bundle 12M-D is nef on the perfect compactification.
In positive characteristic, 12M-D is semi-ample.
The exceptional locus is the closure of abelian varieties with an elliptic factor.
Abstract
The line bundle on the perfect compactification is nef; we show here that in positive characteristic it is semi-ample and that in all characteristics its exceptional locus is the closure of the locus of abelian varieties with an elliptic factor.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Intracerebral and Subarachnoid Hemorrhage Research