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We study certain sequences of moduli spaces of sheaves on K3 surfaces,building on work of Markman, Yoshioka, and Nakajima. We show that thesesequences can be given the structure of a geometric categorical sl_2 action inthe sense of Cautis, Kamnitzer, and Licata. As a corollary, we get anequivalence between derived categories of some moduli spaces that arebirational via stratified Mukai flops.

A categorical sl_2 action on some moduli spaces of sheaves