Fabio Perroni

Irreducibility of the space of dihedral covers of the projective line of a given numerical type

We show in this paper that the set of irreducible components of the family of Galois coverings of P^1_C with Galois group isomorphic to D_n is in bijection with the set of possible numerical types. In this special case the numerical type is the equivalence class (for automorphisms of D_n) of the function which to each conjugacy class \mathcal{C} in D_n associates the number of branch points whose local monodromy lies in the class \mathcal{C}.

The irreducible components of the moduli space of dihedral covers of algebraic curves

In this paper we introduce a new invariant for the action of a finite group

The cohomological crepant resolution conjecture for P(1,3,4,4)

G

CHEN–RUAN COHOMOLOGY OF ADE SINGULARITIES

on a compact complex curve of genus

Automorphisms of rational manifolds of positive entropy with Siegel disks

g

A model for the orbifold Chow ring of weighted projective spaces

. With the aid of this invariant we achieve the classification of the components of the moduli space of curves with an effective action by the dihedral group

Computing certain Gromov-Witten invariants of the crepant resolution of ℙ(1, 3, 4, 4)

D_n

Dihedral Galois covers of algebraic varieties and the simple cases

. This invariant has been used in the meanwhile by the authors in order to extend the genus stabilization result of Livingston and Dunfield and Thurston to the ramified case. This new version contains an appendix clarifying the correspondence between the above components and the image loci in the moduli space M_g (classifying when two such components have the same image).

PSEUDO-AUTOMORPHISMS OF POSITIVE ENTROPY ON THE BLOWUPS OF PRODUCTS OF PROJECTIVE SPACES

We prove the cohomological crepant resolution conjecture of Ruan for the weighted projective space ℙ(1,3,4,4). To compute the quantum corrected cohomology ring, we combine the results of Coates–Corti–Iritani–Tseng on ℙ(1,1,1,3) and our previous results.

Chen-Ruan cohomology of ADE singularities

We study Ruans cohomological crepant resolution conjecture [41] for orbifolds with transversal ADE singularities. In the An-case, we compute both the Chen–Ruan cohomology ring and the quantum corrected cohomology ring H*(Z)(q1,…,qn). The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between and H*(Z)(-1) in the A1-case, verifying Ruans conjecture. In the An-case, the family H*(Z)(q1,…,qn) is not defined for q1 = ⋯ = qn = -1. This implies that the conjecture should be slightly modified. We propose a new conjecture in the An-case (Conjecture 1.9). Finally, we prove Conjecture 1.9 in the A2-case by constructing an explicit isomorphism.