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P=W conjectures for character varieties with symplectic resolution

- Camilla Felisetti, Mirko Mauri
- Mathematics
- 15 June 2020

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… Expand

G-birational superrigidity of Del Pezzo surfaces of degree 2 and 3

- Lucas das Dores, Mirko Mauri
- Mathematics
- European Journal of Mathematics
- 15 August 2018

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 equations… Expand

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 compact… Expand

Constructing local models for Lagrangian torus fibrations

- Jonathan D. Evans, Mirko Mauri
- Mathematics
- 22 May 2019

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 a… Expand

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 of… Expand

The dual complex of log Calabi–Yau pairs on Mori fibre spaces

- Mirko Mauri
- Mathematics
- 10 August 2018

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 of… Expand

Essential skeletons of pairs and the geometric P=W conjecture.

- Mirko Mauri, Enrica Mazzon, Matthew Stevenson
- Mathematics
- 28 October 2018

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-Soibelman… Expand

KODAIRA EMBEDDING THEOREM

- Mirko Mauri
- 2015

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. The… Expand

Lagrangian fibrations

- D. Huybrechts, Mirko Mauri
- Mathematics
- 23 August 2021

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–Yin… Expand

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