
TL;DR
This paper extends the classical Torelli theorem, demonstrating that a curve can be uniquely determined by its Jacobian and certain symmetric power images for a broader range of degrees.
Contribution
It generalizes the Torelli theorem by replacing the symmetric power degree with any integer between 1 and g-1, broadening the theorem's applicability.
Findings
The Torelli theorem holds for all degrees d in 1 to g-1.
The pair (J(C), W^d) determines the curve C for these degrees.
The result unifies and extends previous cases of the theorem.
Abstract
Given a smooth projective curve of genus over the complex numbers, Torelli's thoerem asserts that the pair determines , where is an image of the st symmetric power of inside the Jacobian under an Abel-Jacobi map. We show that the theorem holds with replaced by an integer in the range .
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
TopicsMatrix Theory and Algorithms · Mathematics and Applications · Advanced Optimization Algorithms Research
