Counterexamples to Mercat's Conjecture

2013/06/11 by Akash Kumar Sengupta, Sengupta, Akash Kumar
Mathematics · #14H51 #14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H51 #msc:14H60

paper · pdf · doi:10.48550/arxiv.1306.2553

6 pages, Proof of a lemma added in Section 2, Slight change in the proof of the main theorem, added references

arxiv created 2013/07/30 · arxiv updated 2013/08/01

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.

Related

• The Mercat Conjecture for stable rank 2 vector bundles on generic curves
• Sections of K3 surfaces with Picard number two and Mercat's conjecture
• An effective restriction theorem via wall-crossing and Mercat's conjecture
• Restricted Lazarsfeld-Mukai bundles and canonical curves
• On the correspondence between Ulrich bundles and curves on surfaces