Positivity vs. slope semistability for bundles with vanishing discriminant

Abstract

We give an algebraic proof valid in arbitrary characteristic for the known equivalence between (strongly) slope semistable vector bundles with vanishing discriminant and vanishing determinant and numerically flat bundles. We also address a related question of Misra.

arXiv commentSecond named author added. The main results are extended to arbitrary characteristic. A new counterexample to Misra's question added. An optimistic application of the Mehta-Ramanathan theorem in Corollary 3.2 of the initial submission has been corrected

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Cited by in corpus (1)

• Approximation of semistable bundles on smooth algebraic varieties