Remarks on families of singular curves with hyperelliptic normalizations

We give restrictions on the existence of families of curves on smooth projective surfaces $S$ of nonnegative Kodaira dimension all having constant geometric genus $g \geq 2$ and hyperelliptic normalizations. In particular, we prove a Reider-like result whose proof is ``vector bundle-free'' and relies on deformation theory and bending-and-breaking of rational curves in \Sym^2(S). We also give examples of families of such curves.Comment: 18 page

On the birationality of the adjunction mapping of projective varieties

Let $X$ be a smooth projective $n$-fold such that $q(X)=0$ and $L$ a globally generated, big line bundle on $X$ such that $h^0(K_X+(n-2)L) >0$. We give necessary and sufficient conditions for the adjoint systems $|K_X+kL|$ to be birational for $k \geq n-1$. In particular, for Calabi-Yau $n$-folds we generalize and prove parts of a conjecture of Gallego and Purnaprajna.Comment: 7 pages, accepted for publication in Journal of the Ramanujan Mathematical Societ

Smooth curves on projective K3 surfaces

In this paper we give for all $n \geq 2$, d>0, $g \geq 0$ necessary and sufficient conditions for the existence of a pair (X,C), where X is a K3 surface of degree 2n in \matbf{P}^{n+1} and C is a smooth (reduced and irreducible) curve of degree d and genus g on X. The surfaces constructed have Picard group of minimal rank possible (being either 1 or 2), and in each case we specify a set of generators. For $n \geq 4$ we also determine when X can be chosen to be an intersection of quadrics (in all other cases X has to be an intersection of both quadrics and cubics). Finally, we give necessary and sufficient conditions for \O_C (k) to be non-special, for any integer $k \geq 1$.Comment: 12 pages, to appear in Math. Scand. Mistake in earlier version of Thm 1.1 corrected and its proof is considerably simplified (removed the now redundant Sections 4 and 5 of the previous version). Added Rem. 1.2 and Prop. 1.

Institutional Clash and Financial Fragility. An Evolutionary Model of Banking Crises

There are mainly two types of theories explaining banking crisis, emanating from the monetarist school respectively institutional economics. Using an allegory, monetarists are discussing how much water in terms of liquidity that is needed to stop a fire escalating into a disaster, while institutionalists are occupied with the causes of the fire. Our study rejects the explanatory value of the monetarist view, but also criticizes the Kindleberger-Minsky model for not taking the legalisation and the sanctions in the hands of the authorities into account. We consider the institutional factor as a decisive part in the understanding of systemic risk and the process towards increasing debt in non-financial sectors and introduce the concept institutional clash. Not every recession has caused a banking crisis. But all banking crises have been preceded by an institutional clash. Consequently, an institutional clash is a prerequisite but not sufficient to cause a banking crisis: there must be a recession for a crisis to emerge. We also launch a stage-model for the evolution of banking crises. The stages in that model highlight decisive factors before, under and after a crisis. Our model has the capability to explain the occurrence of crises in a re-regulated economy. However, we only give few examples from Nordic banking crises how our model could be applied. Thus, the article is explorative. It is natural to make further empirical observation in order get a solid theory of driving forces behind banking crisis. The next step would be to empirically integrate all the Nordic banking crises between 1850 and 2000 in our analysis.Banking history, banking crisis, finance, institutional theory, Denmark, Finland, Norway, Sweden, Scandinavia