A CATEGORICAL sl2 ACTION ON SOME MODULI SPACES OF SHEAVES

We study certain sequences of moduli spaces of sheaves on K3 surfaces, building on work of Markman [J. Algebraic Geom. 10 (2001), pp. 623-694], Yoshioka [J. Reine Angew.Math. 515 (1999), pp. 97-123], and Nakajima [Convolution on homology groups of moduli spaces of sheaves on K3 surfaces, Contemp. Math., vol. 322, Amer. Math. Soc., Providence, RI, 2003, pp. 75-87]. We show that these sequences can be given the structure of a geometric categorical sl2 action in the sense of Cautis, Kamnitzer, and Licata. As a corollary, we get an equivalence between derived categories of some moduli spaces that are birational via stratified Mukai flops.