Families of hypersurfaces of large degree

We show that general moving enough families of high enough degree hypersurfaces in a complex projective space do not have a dominant set of sections

Analytic torsion of Hirzebruch surfaces

Using different forms of the arithmetic Riemann-Roch theorem and the computations of Bott-Chern secondary classes, we compute the analytic torsion and the height of Hirzebruch surfaces

Hodge metrics and positivity of direct images

Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle $E$ on a complex manifold, and every positive integer $k$, the vector bundle $S^kE\otimes\det E$ has a continuous metric with Griffiths semi-positive curvature. If $E$ is ample on a projective manifold, the metric can be made smooth and Griffiths positive.Comment: revised and expanded version of "A positivity property of ample vector bundles

What can changes in structural factors tell us about unemployment in Europe?

This paper examines the impact of temporal variation in labour market institutions and other structural factors on unemployment in Europe. These include the influence of trade unions, social security benefits, employment security, mismatch between job seekers and vacancies, the minimum wage and factors which drive a wedge between consumer and producer prices. With this aim, a system including a labour demand and a wage equation is estimated in pooled time-series data for the six largest EU countries for the 1980s and 1990s, allowing for country-specific fixed-effects, institutional effects and adjustment terms. Our estimates suggest that changes in regional mismatch, trade union density and the ratio between consumer and producer prices are positively associated with structural unemployment. This result is robust to a wide variety of different specifications of the model, including a larger sample of eight EU countries. No consistent role is found for the other institutional factors. JEL Classification: E24, J30, C33Labour market institutions, panel estimation, structural unemployment

Stability of restrictions of cotangent bundles of irreducible Hermitian symmetric spaces of compact type

It is known that the cotangent bundle $\Omega_Y$ of an irreducible Hermitian symmetric space $Y$ of compact type is stable. Except for a few obvious exceptions, we show that if $X \subset Y$ is a complete intersection such that $Pic(Y) \to Pic(X)$ is surjective, then the restriction $\Omega_{Y|X}$ is stable. We then address some cases where the Picard group increases by restriction.Comment: Results and exposition improve

BCOV invariants of Calabi--Yau manifolds and degenerations of Hodge structures

Calabi--Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky--Cecotti--Ooguri--Vafa (BCOV), it is expected that genus 1 curve counting on a Calabi--Yau manifold is related to a conjectured invariant, only depending on the complex structure of the mirror, and built from Ray--Singer holomorphic analytic torsions. To this end, extending work of Fang--Lu--Yoshikawa in dimension 3, we introduce and study the BCOV invariant of Calabi--Yau manifolds of arbitrary dimension. To determine it, knowledge of its behaviour at the boundary of moduli spaces is imperative. We address this problem by proving precise asymptotics along one-parameter degenerations, in terms of topological data and intersection theory. Central to the approach are new results on degenerations of $L^2$ metrics on Hodge bundles, combined with information on the singularities of Quillen metrics in our previous work.Comment: Minor revision. Mainly restructure of the text, minor improvements and corrections. Added information about subdominant terms of $L^2$-norm

How Do Institutions Affect Structural Unemployment in Times of Crises?

This paper examines the effect of economic crises on structural unemployment using an Autoregressive Distributed Lags model and accounting for the role of institutional settings on an unbalanced panel of 30 OECD economies from 1960 to 2006. We found that downturns have, on average, a significant positive impact on the level of structural unemployment rate. The maximum impact varies with the severity of the downturn. Institutions (such as employment protection legislation, average replacement ratio and product market regulation) influence both the extent of the initial shock and the adjustment pattern in the aftermath of an economic downtu

Exponential localization of Wannier functions in insulators

The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified.Comment: Four pages, two figure