47 research outputs found
Smooth covers of moduli stacks of Riemann surfaces with symmetry
No full textWe construct explicitly a finite cover of the moduli stack of compact Riemann surfaces with a given group of symmetries by a smooth quasi-projective variety
Orbifold Cohomology of ADE-singularities
No full textIn Chapter 1 we collect some basic definitions on orbifolds, morphisms of orbifolds and orbifold vector bundles. In Chapter 3 we first review the definition of orbifold cohomology ring for a complex orbifold, then we state the cohomological crepant resolution conjecture as given by Ruan in [52]. In Chapter 4 we define orbifolds with transversal ADE-singularities, see Definition 4.2.5. Then we give a description of the twisted sectors in general.
Finally we specialize to orbifolds with transversal A_n-singularities and, under the technical assumption of trivial monodromy, we compute the orbifold cohomology ring. In Chapter 5 we study the crepant resolution. We first show
that any variety with transversal ADE-singularities Y has a unique crepant resolution p : Z --> Y, Proposition 5. 2 .1. Then we restrict our attention to the case of transversal An-singularities and trivial monodromy and we give an explicit description of the cohomology ring of Z. Chapter 6 contains the computations of the Gromov-Witten invariants of Z in the A_n case. We also give a description of the quantum corrected cohomology ring of Z. In Chapter
7 we prove Ruan's conjecture in the Ai case and, in the A2 case with minor modifications
Automorphisms of rational manifolds of positive entropy with Siegel disks
No full textUsing McMullen’s rational surface automorphisms, we construct projective rational manifolds of higher dimension admitting automorphisms of positive entropy with arbitrarily high number of Siegel disks and those with exactly one Siegel disk
The fundamental group of a quotient of a product of curves
No full textWe prove a structure theorem for the fundamental group of the quotient X of a product of curves by the action of a finite group G and, hence, for that of any resolution of the singularities of X
On the Motivic Class of the Moduli Stack of Twisted -Covers
No full textWe describe the class, in the Grothendieck group of stacks, of the stack of
twisted -covers of genus curves, in terms of the loci corresponding to
covers over smooth bases
Dihedral Galois covers of algebraic varieties and the simple cases
No full textIn this article we investigate the algebra and geometry of dihedral covers of smooth algebraic varieties. To this aim we first describe the Weil divisors and the Picard group of divisorial sheaves on normal double covers. Then we provide a structure theorem for dihedral covers, that is, given a smooth variety Y, we describe the algebraic “building data” on Y which are equivalent to the existence of such covers π:X→Y. We introduce then two special very explicit classes of dihedral covers: the simple and the almost simple dihedral covers, and we determine their basic invariants. For the simple dihedral covers we also determine their natural deformations. In the last section we give an application to fundamental groups
Il corso di Matematica proposto dal Polo di Trieste del Progetto “I Lincei per una nuova didattica nella scuola: una rete nazionale” nell’a. a. 2019-20
No full textCronaca del corso di Matematica proposto dal Polo di Trieste del Progetto “I Lincei per una nuova didattica nella scuola: una rete nazionale” nell’a. a. 2019-20, con qualche riflessione finale
Irreducibility of the space of dihedral covers of the projective line of a given numerical type
No full textWe show in this paper that the set of irreducible components of the family of Galois coverings of \bP1\bC with Galois group isomorphic to \Dn is in bijection with the set of possible numerical types. In this special case the numerical type is the equivalence class (for automorphisms of \Dn) of the function which to each conjugacy class \sC in \Dn associates the number of branch points whose local monodromy lies in the class \sC
CYCLIC AND ABELIAN COVERINGS OF REAL VARIETIES
No full textWe describe the birational and the biregular theory of cyclic and Abelian coverings between real varieties
