Reider's Theorem and Thaddeus Pairs Revisited

Details Reider's Theorem and Thaddeus Pairs Revisited Reider's Theorem and Thaddeus Pairs Revisited

2009-04-22

arxiv.org/abs/0904.3500v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

Bridgeland stability conditions allow for a new generalization of Thaddeus pairs to surfaces and a new interpretation of Reider's theorem as a consequence of "Schur's lemma" for stable objects (Hom(E,F) = 0 if E,F are stable objects and the slope of E exceeds the slope of F). One improvement of Reider's theorem results (Proposition 3.8/Corollary 3.9), and wall-crossings for the new Thaddeus pairs are discussed. This paper was submitted to the CMI conference proceedings celebrating the 65th birthday of Peter Newstead.

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