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Codes over Galois Ring Gilberto Bini We shall briefly recall some basic facts on trace codes over finite fields. In particular, we will focus on generalizations of dual Melas codes. After such an overview, we will introduce the Galois ring set-up in which we try to extend some of the techniques over fields. For these purposes, we need some results on… (More)

- Gilberto Bini
- 2004

For a partition λ = {λ1 ≥ λ2 ≥ λ3 ≥ 0} of non-negative integers, we calculate the Euler characteristic of the local system Vλ on the moduli space of genus 3 hyperelliptic curves using a suitable stratification. For some λ of low degree, we make a guess for the motivic Euler characteristic of Vλ using counting curves over finite fields.

In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves. The proof relies on quite elementary methods, such as the enumeration of the graphs involved in a suitable stratification of M2,n.

- Gilberto Bini
- 2003

On the moduli space of curves we consider the cohomology classes μj(s), s ∈ N, s ≥ 2, which can be viewed as a generalization of the Hodge classes λi defined by Mumford in [6]. Following the methods used in this paper, we prove that the μj(s) belong to the tautological ring of the moduli space. MSC 2000: 14H10 (primary); 14C40, 19L10, 19L64 (secondary)

We focus on the rational cohomology of Cornalba’s moduli space of spin curves of genus 1 with n marked points. In particular, we show that both its first and its third cohomology group vanish and the second cohomology group is generated by boundary classes.

Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type (p, 0) and on computations of the Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the… (More)

- Gilberto Bini, John Harer
- 1986

Let Mng be the moduli space of n-pointed Riemann surfaces of genus g. Denote by M n g the Deligne-Mumford compactification of Mng . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of M n g for any g and n such that n > 2− 2g.

- Gilberto Bini
- 2002

As pointed out in Arbarello and Cornalba (J. Alg. Geom. 5 (1996), 705–749), a theorem due to Di Francesco, Itzykson, and Zuber (see Di Francesco, Itzykson, and Zuber, Commun. Math. Phys. 151 (1993), 193–219) should yield new relations among cohomology classes of the moduli space of pointed curves. The coefficients appearing in these new relations can be… (More)

- Gilberto Bini, Tyler Kelly
- 2008

In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard Fuchs equation associated to the holomorphic 3-form. In this paper we give an easy argument, involving the family of Mirror Quintics, which implies this… (More)

- Gilberto Bini
- Des. Codes Cryptography
- 2006