Modular Forms and Special Cubic Fourfolds

We study the degree of the special cubic fourfolds in the Hilbert scheme of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signature (2, 20).Comment: 13 page

Exports, Productivity, and Credit Constraints : A Firmâ€ÂLevel Empirical Investigation of China

Recent Melitz-type (2003) intra-industry heterogonous trade models argue that a firm's productivity has significant effects on the firm's exports. This paper examines how a firms credit constraints as well as its productivity affect its export decisions. We imbed the firm's credit constraints into a Melitz-type general-equilibrium model by endogenizing the probability of the success of firm-specific projects. We show that, all else equal, it is easier for firms to enter the export market if (1) the probability of the success of their project is higher and consequently they have easier access to external finance from financial intermediaries; or (2) they have alternative sources, other than from financial intermediaries, to obtain funds. We test these theoretical hypotheses using firm-level data from Chinese manufacturing industries and find strong evidence supporting the predictions of the model.Credit Constraints, Heterogeneous Firms, productivity, trade

Picard groups on moduli of K3 surfaces with Mukai models

We discuss the Picard group of moduli space $\mathcal{K}_g$ of quasi-polarized K3 surfaces of genus $g\leq 12$ and $g\neq 11$. In this range, $\mathcal{K}_g$ is unirational and a general element in $\mathcal{K}_g$ is a complete intersection with respect to a vector bundle on a homogenous space, by the work of Mukai. In this paper, we find generators of the Picard group $Pic_\mathbb{Q}(\mathcal{K}_g)$ using Noether-Lefschetz theory. This verifies the Noether-Lefschetz conjecture on moduli of K3 surfaces in these cases.Comment: fix some typo