Abstract
Recently, Lomadze, Ravi, Rosenthal and Schumacher gave a natural and geometrically meaningful one-to-one correspondence between abstract linar behaviors and coherent sheaves on P1. Motivated by their result, here we give a complete picture of the deformation theory of coherent sheaves on P1. We use our results to study deformations over the field R obtaining a connectedness result for the real locus of the algebraic parameter spaces.
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