A Counterexample for Subadditivity of Multiplier Ideals on Toric Varieties
Jen-Chieh Hsiao
TL;DR
This paper presents a counterexample in three-dimensional toric varieties showing subadditivity of multiplier ideals can fail, and provides a combinatorial proof for the two-dimensional case.
Contribution
It constructs the first known counterexample in 3D and offers a combinatorial proof for 2D cases of subadditivity of multiplier ideals.
Findings
Counterexample in 3D toric variety where subadditivity fails
Proof of subadditivity in 2D normal toric varieties
Clarification of conditions under which subadditivity holds or fails
Abstract
We construct a 3-dimensional complete intersection toric variety on which the subadditivity formula doesn't hold, answering negatively a question by Takagi and Watanabe. A combinatorial proof of the subadditivity formula on 2-dimensional normal toric varieties is also provided.
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 · Commutative Algebra and Its Applications · Polynomial and algebraic computation