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Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology
A quick journey on stable sheaves and vector bundles
In this article, we collect main results obtained from our collaboration with Edoardo Ballico. The topics cover various aspects on the theory of vector bundles and stable sheaves related to Castelnuovo–Mumford regularity, cohomological splitting criteria, globally generated vector bundles, arithmetically Cohen–Macaulay sheaves, logarithmic vector bundles, stable sheaves of rank zero and co-Higgs sheaves
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