Chern Classes of the Moduli Stack of Curves

Here we calculate the Chern classes of ${\bar {\mathcal M}}_{g,n}$, the moduli stack of stable n-pointed curves. In particular, we prove that such classes lie in the tautological ring.Comment: submitted preprin

On the rational cohomology of moduli spaces of curves with level structures

We investigate low degree rational cohomology groups of smooth compactifications of moduli spaces of curves with level structures. In particular, we determine H^k(\sgbar, \Q) for $g \ge 2$ and $k \le 3$, where \sgbar denotes the moduli space of spin curves of genus $g$.Comment: Final version accepted for publication on Geometriae Dedicat

New Fourfolds from F-Theory

In this paper, we apply Borcea-Voisin's construction and give new examples of fourfolds containing a del Pezzo surface of degree six, which admit an elliptic fibration on a smooth threefold. Some of these fourfolds are Calabi-Yau varieties, which are relevant for the $N=1$ compactification of Type IIB string theory known as $F$-Theory. As a by-product, we provide a new example of a Calabi--Yau threefold with Hodge numbers $h^{1,1}=h^{2,1}=10$.Comment: 12 Pages, 1 Figure, to appear in Math. Nac

Diffeomorphism classes of Calabi-Yau varieties

In this article we investigate diffeomorphism classes of Calabi-Yau threefolds. In particular, we focus on those embedded in toric Fano manifolds. Along the way, we give various examples and conclude with a curious remark regarding mirror symmetry.Comment: 10 pages; v2 minor changes: typos and exposition improved; to appear in Rendiconti del Seminario Matematic