Families of nodal curves on projective threefolds and their regularity via postulation of nodes

The main purpose of this paper is to introduce a new approach to study families of nodal curves on projective threefolds. Precisely, given $X$ a smooth projective threefold, \E a rank-two vector bundle on $X$, $L$ a very ample line bundle on $X$ and $k \geq 0$, $\delta >0$ integers and denoted by V= {\V}_{\delta} ({\E} \otimes L^{\otimes k}) the subscheme of {\Pp}(H^0({\E} \otimes L^{\otimes k})) parametrizing global sections of {\E} \otimes L^{\otimes k} whose zero-loci are irreducible and $\delta$-nodal curves on $X$, we present a new cohomological description of the tangent space T_{[s]}({\V}_{\delta} ({\E} \otimes L^{\otimes k})) at a point [s]\in {\V}_{\delta} ({\E} \otimes L^{\otimes k}). This description enable us to determine effective and uniform upper-bounds for $\delta$, which are linear polynomials in $k$, such that the family $V$ is smooth and of the expected dimension ({\em regular}, for short). The almost-sharpness of our bounds is shown by some interesting examples. Furthermore, when $X$ is assumed to be a Fano or a Calaby-Yau threefold, we study in detail the regularity property of a point $[s] \in V$ related to the postulation of the nodes of its zero-locus $C_s =C \subset X$. Roughly speaking, when the nodes of $C$ are assumed to be in general position either on $X$ or on an irreducible divisor of $X$ having at worst log-terminal singularities or to lie on a l.c.i. and subcanonical curve in $X$, we find upper-bounds on $\delta$ which are, respectively, cubic, quadratic and linear polynomials in $k$ ensuring the regularity of $V$ at $[s]$. Finally, when X= \Pt, we also discuss some interesting geometric properties of the curves given by sections parametrized by $V$.Comment: 28 pages, typos added. To appear on Trans.Amer. Math. So

P^r-scrolls arising from Brill-Noether theory and K3-surfaces

In this paper we study examples of P^r-scrolls defined over primitively polarized K3 surfaces S of genus g, which arise from Brill-Noether theory of the general curve in the primitive linear system on S and from classical Lazarsfeld's results in. We show that such scrolls form an open dense subset of a component H of their Hilbert scheme; moreover, we study some properties of H (e.g. smoothness, dimensional computation, etc.) just in terms of the moduli space of such K3's and of the moduli space of semistable torsion-free sheaves of a given Mukai-vector on S. One of the motivation of this analysis is to try to introducing the use of projective geometry and degeneration techniques in order to studying possible limits of semistable vector-bundles of any rank on a general K3 as well as Brill-Noether theory of vector-bundles on suitable degenerations of projective curves. We conclude the paper by discussing some applications to the Hilbert schemes of geometrically ruled surfaces whose base curve has general moduli.Comment: published in Manuscripta Mathematic

Moduli of nodal curves on smooth surfaces of general type

In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by V(|D|, \delta)), which parametrize universal families of irreducible, \delta-nodal curves in a complete linear system |D|, on a smooth projective surface S of general type. We determine geometrical and numerical conditions on D and numerical conditions on \delta ensuring that such number coincides with dim(V(|D|, \delta). As related facts, we also determines some sharp results concerning the geometry of some Severi varieties.Comment: Latex2e, 27 page

Price Stickiness Asymmetry, Persistence and Volatility in a New Keynesian Model

In a two-sector New-Keynesian model, this paper shows that the dispersion in the degree of sectoral price stickiness plays a key role in the determination of the dynamics of aggregate inflation and, consequently, of the whole economy. The dispersion in price stickiness reduces the persistence of inflation and, to a smaller extent, of the interest rate. It also reduces the volatility of inflation, the interest rate and the output-gap. Thus two economies with the same average degree of price stickiness but a different variance may behave very differently, highlighting the relevance of sectoral data for economic estimations and forecasts.Sectoral asymmetries, price stickiness, New Keynesian model, persistence, volatility.

Transmission Lags and Optimal Monetary Policy

Real world monetary policy is complicated by long and variable lags in the transmission of the policy to the economy. Most of the policy models, however, abstracts from policy lags. This paper presents a model where transmission lags depend on the behaviour of a two-sector supply side of the economy and focuses on how lag length and variability affect optimal monetary policy. The paper shows that optimal monetary policy should respond more to the sector with the shortest transmission lag and that the presence of production links among sectors amplifies this response. Furthermore, the shorter or more variable the aggregate transmission lag, the more active the overall policy and the larger the response to the sector with the shortest transmission lag. Finally, the relative strength of the response to inflation and output gap depends on the intensity of the sectoral production links, and on the length of the transmission lags. Only with reasonable production links should the optimal policy respond more to in?ation than to the output gap in line with the empirical evidence.Inflation targeting; monetary policy transmission mechanism; policy transmission lags; multiplicative uncertainty; Markov jump linear quadratic systems; optimal monetary policy.

CPI Inflation Targeting and Exchange Rate Pass-through

This paper analyzes how imperfect exchange rate pass-through affects the transmission of the CPI inflation targeting optimal monetary policy. In the short run, delayed pass-through constraints monetary policy more than incomplete pass-through and interest rate smoothing amplifies this effect. In addition, imperfect pass-through does not increase the variability of the real exchange rate for a subset of strict CPI inflation targeting cases and for flexible CPI inflation targeting. Furthermore, there exists an inverse relation between the pass-through and the insulation of CPI inflation from foreign shocks, and when the pass-through falls, the impact on the trade-off between the stabilization of both CPI inflation and output depends on how strictly the central bank is targeting CPI inflation and on the kind of imperfect pass-through.Inflation Targeting; Exchange Rate Pass-through; Open-economy; Direct Exchange Rate Channel; Optimal Monetary Policy.

Household's Preferences and Monetary Policy Inertia

The estimation of monetary policy rules suggests that the interest rates set by central banks move with a certain inertia. Although a number of hypotheses have been suggested to explain this phenomenon, its ultimate origin is unclear, thus delineating this issue as a modern "puzzle" in monetary economics. We show that household's preferences can play an important role in determining optimal interest rate inertia. Importantly, this can occur even when the central bank has egligible preferences for smoothing the interest rate

Extensions of line bundles and Brill--Noether loci of rank-two vector bundles on a general curve

In this paper we study Brill-Noether loci for rank-two vector bundles and describe the general member of some components as suitable extensions of line bundles.Comment: 31 pages; revised version after referees' comments; to appear in Revue Roumaine de Math\'ematiques Pures et Appliqu\'ee

Genera of curves on a very general surface in P3P^3

In this paper we consider the question of determining the geometric genera of irreducible curves lying on a very general surface $S$ of degree $d$ at least 5 in $\mathbb{P}^3$ (the cases $d \leqslant 4$ are well known). We introduce the set $Gaps(d)$ of all non-negative integers which are not realized as geometric genera of irreducible curves on $S$. We prove that $Gaps(d)$ is finite and, in particular, that $Gaps(5)= \{0,1,2\}$. The set $Gaps(d)$ is the union of finitely many disjoint and separated integer intervals. The first of them, according to a theorem of Xu, is $Gaps_0(d):=[0, \frac{d(d-3)}{2} - 3]$. We show that the next one is $Gaps_1(d):= [\frac{d^2-3d+4}{2}, d^2-2d-9]$ for all $d \geqslant 6$.Comment: 16 page

Equivalence of families of singular schemes on threefolds and on ruled fourfolds

The main purpose of this paper is twofold. We first want to analyze in details the meaningful geometric aspect of the method introduced in the previous paper [12], concerning regularity of families of irreducible, nodal "curves" on a smooth, projective threefold $X$. This analysis highlights several fascinating connections with families of other singular geometric "objects" related to $X$ and to other varieties. Then, we generalize this method to study similar problems for families of singular divisors on ruled fourfolds suitably related to $X$.Comment: 22 pages, Latex 2e, submitted preprin