Rational Lagrangian fibrations on punctual Hilbert schemes of K3 surfaces |
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Authors: | Dimitri Markushevich |
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Institution: | (1) Mathématiques - bât.M2, Université Lille 1, 59655 Villeneuve d'Ascq Cedex, France |
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Abstract: | A rational Lagrangian fibration f on an irreducible symplectic variety V is a rational map which is birationally equivalent to a regular surjective morphism with Lagrangian fibers. By analogy with K3 surfaces, it is natural to expect that a rational Lagrangian fibration exists if and only if V has a divisor D with Bogomolov–Beauville square 0. This conjecture is proved in the case when V is the Hilbert scheme of d points on a generic K3 surface S of genus g under the hypothesis that its degree 2g−2 is a square times 2d−2. The construction of f uses a twisted Fourier–Mukai transform which induces a birational isomorphism of V with a certain moduli space of twisted sheaves on another K3 surface M, obtained from S as its Fourier–Mukai partner. |
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Keywords: | 14J60 14J40 |
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