Rational Lagrangian fibrations on punctual Hilbert schemes of K3 surfaces
| dc.creator | Markushevich, D. | |
| dc.date | 2005-09-15 | |
| dc.date | 2007-03-06 | |
| dc.date.accessioned | 2026-07-07T07:50:06Z | |
| dc.date.available | 2026-07-07T07:50:06Z | |
| dc.description | A rational Lagrangian fibration f on an irreducible symplecitc 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 punctual Hilbert scheme of a generic algebraic K3 surface S. 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. | |
| dc.description | Final version; minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0509346 | |
| dc.identifier | http://arxiv.org/abs/math/0509346 | |
| dc.identifier | Manuscripta Math. 120 (2006), no. 2, 131--150 | |
| dc.identifier | doi:10.1007/s00229-006-0631-4 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125058 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J60, 14J40 | |
| dc.title | Rational Lagrangian fibrations on punctual Hilbert schemes of K3 surfaces | |
| dc.type | text |