论文标题
p =具有符号分辨率的角色品种的构想
P=W conjectures for character varieties with symplectic resolution
论文作者
论文摘要
我们建立了具有结构组$ \ mathrm {gl} _n $和$ \ mathrm {sl} _n $的p = w and pi = wi costofors thust symplectic分辨率，即属1和属1和任意等级，以及p = 2。我们利用了希格斯捆绑包的多尔贝特模量空间的异性和准泰尔修饰的拓扑。为此，我们证明了独立兴趣的辅助结果，例如用于还原代数基团的Hodge模量空间的相对压实以及De Rham Moduli空间的压缩的预测性。特别是，我们详细研究了一个多元模量空间，该空间是O'Grady 6型的奇异不可塑态象征性品种的专业化。
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-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, and the projectivity of the compactification of the de Rham moduli space. 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.
