On positivity and semistability of vector bundles in finite and mixed characteristics

Abstract

We survey results concerning behavior of positivity of line bundles and possible vanishing theorems in positive characteristic. We also try to describe variation of positivity in mixed characteristic. These problems are very much related to behavior of strong semistability of vector bundles, which is another main topic of the paper.

27 pages, dedicated to C.S. Seshardi on his 20th birthday (in this rare case the number of years does not coincide with the number of birthdays); v2: updated references and added footnotes

References in corpus (2)

• Semistability and Hilbert-Kunz multiplicities for curves
• On a positive equicharacteristic variant of the $p$-curvature conjecture

Cited by in corpus (8)

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• Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties
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• A Mehta-Ramanathan theorem for linear systems with basepoints
• Slope inequality for families of curves over surfaces
• Complete families of smooth space curves and strong semistability
• Arithmetically nef line bundles