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P=W conjectures for character varieties with symplectic resolution
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, andExpand
G-birational superrigidity of Del Pezzo surfaces of degree 2 and 3
Any minimal Del Pezzo G-surface S of degree smaller than 3 is G-birationally rigid. We classify those which are G-birationally superrigid, and for those which fail to be so, we describe the equationsExpand
INTERSECTION COHOMOLOGY OF RANK 2 CHARACTER VARIETIES OF SURFACE GROUPS
  • Mirko Mauri
  • Mathematics
  • Journal of the Institute of Mathematics of…
  • 12 January 2021
For $G = \mathrm {GL}_2, \mathrm {SL}_2, \mathrm {PGL}_2$ we compute the intersection E-polynomials and the intersection Poincaré polynomials of the G-character variety of a compactExpand
Constructing local models for Lagrangian torus fibrations
We give a construction of Lagrangian torus fibrations with controlled discriminant locus on certain affine varieties. In particular, we apply our construction in the following ways. We find aExpand
Topological mirror symmetry for rank two character varieties of surface groups
  • Mirko Mauri
  • Mathematics
  • Abhandlungen aus dem Mathematischen Seminar der…
  • 12 January 2021
The moduli spaces of flat $${\text{SL}}_2$$ SL 2 - and $${\text{PGL}}_2$$ PGL 2 -connections are known to be singular SYZ-mirror partners. We establish the equality of Hodge numbers ofExpand
The dual complex of log Calabi–Yau pairs on Mori fibre spaces
In this paper we show that the dual complex of a dlt log Calabi-Yau pair $(Y, \Delta)$ on a Mori fibre space $\pi: Y \to Z$ is a finite quotient of a sphere, provided that either the Picard number ofExpand
Essential skeletons of pairs and the geometric P=W conjecture.
We construct weight functions on the Berkovich analytification of a variety over a trivially-valued field of characteristic zero, and this leads to the definition of the Kontsevich-SoibelmanExpand
KODAIRA EMBEDDING THEOREM
The aim of this report is to prove Kodaira embedding theorem: Theorem 0.1 (Kodaira Embedding Theorem). A compact Kähler manifold endowed with a positive line bundle admits a projective embedding. TheExpand
Lagrangian fibrations
We review the theory of Lagrangian fibrations of hyperkähler manifolds as initiated by Matsushita [Mat99, Mat01, Mat05]. We also discuss more recent work of Shen–Yin [SY18] and Harder–Li–Shen–YinExpand
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