TL;DR
This paper proves a conjecture that smooth projective curves of genus at least 1 have diagonal dimension 2, clarifying a key property related to their geometric complexity.
Contribution
It confirms Conjecture 4.16 from [EL21], establishing the diagonal dimension for a broad class of algebraic curves.
Findings
Smooth projective curves of genus ≥ 1 have diagonal dimension 2.
The result verifies a previously conjectured property in algebraic geometry.
The proof advances understanding of derived categories of curves.
Abstract
We prove Conjecture 4.16 of the paper [EL21] of Elagin and Lunts; namely, that a smooth projective curve of genus at least 1 over a field has diagonal dimension 2.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Vietnamese History and Culture Studies