Subadditivity of Kodaira dimension does not hold in positive characteristic
Paolo Cascini, Sho Ejiri, J\'anos Koll\'ar, and Lei Zhang
TL;DR
This paper constructs examples in positive characteristic algebraic geometry where the expected subadditivity of Kodaira dimension fails, challenging a common assumption in the field.
Contribution
It provides explicit examples showing that subadditivity of Kodaira dimension does not always hold in positive characteristic, which was previously unknown.
Findings
Examples of fibrations violating subadditivity
Counterexamples in positive characteristic
Challenges to existing conjectures
Abstract
Over any algebraically closed field of positive characteristic, we construct examples of fibrations violating subadditivity of Kodaira dimension.
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 · Advanced Algebra and Geometry · Geometry and complex manifolds