Counterexamples to Mercat's Conjecture
Akash Kumar Sengupta
TL;DR
This paper presents counterexamples involving curves on K3 surfaces and vector bundles that disprove Mercat's conjecture for ranks greater than 3.
Contribution
It introduces explicit counterexamples for Mercat's conjecture on K3 surfaces for all ranks n > 3.
Findings
Counterexamples for all n > 3
Curves on K3 surfaces with specific vector bundles
Invalidation of Mercat's conjecture in these cases
Abstract
For any n>3, we provide examples of curves lying on K3 surfaces and vector bundles on those curves which invalidate Mercat's conjecture for rank n bundles.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · North African History and Literature