%0 Generic %1 felisetti2020conjectures %A Felisetti, Camilla %A Mauri, Mirko %D 2020 %K p=w %T P=W conjectures for character varieties with symplectic resolution %U http://arxiv.org/abs/2006.08752 %X We establish P=W and PI=WI conjectures for character varieties with structural group $GL_n$ and $SL_n$ which admit a symplectic resolution, i.e. for genus 1 and arbitrary rank, and genus 2 and rank 2. We formulate the P=W conjecture for resolution, and prove it for symplectic resolutions. We exploit the topology of birational and quasi-étale modifications of Dolbeault moduli spaces of Higgs bundles. To this end, we prove auxiliary results of independent interest, like the construction of a relative compactification of the Hodge moduli space for reductive algebraic groups, or the intersection theory of some singular Lagrangian cycles. In particular, we study in detail a Dolbeault moduli space which is specialization of the singular irreducible holomorphic symplectic variety of type O'Grady 6.

@misc{felisetti2020conjectures, abstract = {We establish P=W and PI=WI conjectures for character varieties with structural group $\mathrm{GL}_n$ and $\mathrm{SL}_n$ which admit a symplectic resolution, i.e. for genus 1 and arbitrary rank, and genus 2 and rank 2. We formulate the P=W conjecture for resolution, and prove it for symplectic resolutions. We exploit the topology of birational and quasi-\'{e}tale modifications of Dolbeault moduli spaces of Higgs bundles. To this end, we prove auxiliary results of independent interest, like the construction of a relative compactification of the Hodge moduli space for reductive algebraic groups, or the intersection theory of some singular Lagrangian cycles. In particular, we study in detail a Dolbeault moduli space which is specialization of the singular irreducible holomorphic symplectic variety of type O'Grady 6.}, added-at = {2020-06-17T09:08:47.000+0200}, author = {Felisetti, Camilla and Mauri, Mirko}, biburl = {https://www.bibsonomy.org/bibtex/2387d1cca8374fdb18ebab31faed7108c/simonechiarello}, description = {P=W conjectures for character varieties with symplectic resolution}, interhash = {4e8bc096376dad939fd52326fc9d7192}, intrahash = {387d1cca8374fdb18ebab31faed7108c}, keywords = {p=w}, note = {cite arxiv:2006.08752Comment: 60 pages, 3 figures}, timestamp = {2020-06-17T09:08:47.000+0200}, title = {P=W conjectures for character varieties with symplectic resolution}, url = {http://arxiv.org/abs/2006.08752}, year = 2020 }