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Creators/Authors contains: "Sawon, Justin"

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  1. ; (, Bulletin of the London Mathematical Society)
    Abstract Suppose that a Hilbert scheme of points on a K3 surface of Picard rank one admits a rational Lagrangian fibration. We show that if the degree of the surface is sufficiently large compared to the number of points, then the Hilbert scheme is the unique hyperkähler manifold in its birational class. In particular, the Hilbert scheme is a Lagrangian fibration itself, which we realize as coming from a (twisted) Beauville–Mukai system on a Fourier–Mukai partner of . We also show that when the degree of the surface is small our method can be used to find all birational models of the Hilbert scheme. 
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  2. ; (, Mathematische Zeitschrift)
    We study wall-crossing for the Beauville–Mukai system of rank three on a general genus two K3 surface. We show that such a system is related to the Hilbert scheme of ten points on the surface by a sequence of flops, whose exceptional loci can be described as Brill–Noether loci. We also obtain Brill–Noether type results for sheaves in the Beauville–Mukai system. 
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  3. (, Experimental Mathematics)
    We conjecture that certain curvature invariants of compact hyperkähler manifolds are positive/negative. We prove the conjecture in complex dimension four, give an “experimental proof” in higher dimensions, and verify it for all known hyperkähler manifolds up to dimension eight. As an application, we show that our conjecture leads to a bound on the second Betti number in all dimensions. 
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  4. (, Communications in Contemporary Mathematics)
    Let [Formula: see text] be a (holomorphic) Lagrangian fibration that is very general in the moduli space of Lagrangian fibrations. We conjecture that the singular fibers in codimension one must be semistable degenerations of abelian varieties. We prove a partial result towards this conjecture, and describe an example that provides further evidence. 
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  5. (, European Journal of Mathematics)
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  6. ; (, Bulletin of the London Mathematical Society)
  7. (, Revista Matemática Contemporânea)
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  8. (, Journal of Geometry and Physics)
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  9. (, Journal of Algebraic Geometry)
    We consider (holomorphic) Lagrangian fibrations π<#comment/> : X →<#comment/> P n \pi :X\rightarrow \mathbb {P}^n that satisfy some natural hypotheses. We prove that there are only finitely many such Lagrangian fibrations up to deformation. 
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  10. ; ; ; (, Springer International Publishing)
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