Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor D(S) -> D(M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of D(M), and that this autoequivalence can be factored into geometrically meaningful equivalences associated to abelian fibrations and Mukai flops. Along the way we produce a derived equivalence between two compact hyperkaehler 2g-folds that are not birational, for every g >= 2. We also speculate about an approach to showing that birational moduli spaces of sheaves on K3 surfaces are derived-equivalent.Comment: 28 pages. typos corrected. final version to appear in JLM

Nef divisors for moduli spaces of complexes with compact support

In [BM14b], the first author and Macr\`i constructed a family of nef divisors on any moduli space of Bridgeland-stable objects on a smooth projective variety X. In this article, we extend this construction to the setting of any separated scheme Y of finite type over a field, where we consider moduli spaces of Bridgeland-stable objects on Y with compact support. We also show that the nef divisor is compatible with the polarising ample line bundle coming from the GIT construction of the moduli space in the special case when Y admits a tilting bundle and the stability condition arises from a \theta-stability condition for the endomorphism algebra. Our main tool generalises the work of Abramovich--Polishchuk [AP06] and Polishchuk [Pol07]: given a t-structure on the derived category D_c(Y) on Y of objects with compact support and a base scheme S, we construct a constant family of t-structures on a category of objects on YxS with compact support relative to S.Comment: 36 pages. In memory of Johan Louis Dupont. V2: updated following comments from the referee and from Joe Karmazyn who gave a counterexample to a false claim in version 1. To appear in Selecta Mat

Insuflon versus subcutaneous injection for cytokine administration in children and adolescents: a randomised crossover study

© 2004 Association of Pediatric Hematology/Oncology NursesPain is a frequent complication of subcutaneous cytokine injections in children. A randomized crossover trial was conducted to determine the least painful and preferred method of cytokine administration for children and young people. The current standard practice of subcutaneous injection was compared with the use of Insuflon (Maersk Medical, Roskilde, Denmark), a subcutaneous indwelling catheter. Children aged between 1 month and 18 years undergoing treatment within the oncology/hematology unit of a single tertiary hospital and receiving cytokines were eligible for the study. Twenty children participated in the study, each child receiving both administration methods in random order during sequential cytokine treatment courses. There was a trend toward higher pain scores when using subcutaneous injections for drug administration compared to Insuflon. Seventy-five percent (n = 15) of the children who completed the trial and their families preferred using Insuflon for subcutaneous drug administration. Consideration needs to be given, however, to those who refused to enter the study, withdrew, or continued because of a preference for subcutaneous injections. Current practice at the Women’s and Children’s Hospital is to allow the child and parents to choose their preferred treatment modality for subcutaneous drug administration