Effective cones of cycles on blow-ups of projective space

In this paper, we study the cones of higher codimension (pseudo)effective cycles on point blow-ups of projective space. We determine bounds on the number of points for which these cones are generated by the classes of linear cycles, and for which these cones are finitely generated. Surprisingly, we discover that for (very) general points, the higher codimension cones behave better than the cones of divisors. For example, for the blow-up $X_r^n$ of $\mathbb P^n$, $n>4$, at $r$ very general points, the cone of divisors is not finitely generated as soon as $r> n+3$, whereas the cone of curves is generated by the classes of lines if $r \leq 2^n$. In fact, if $X_r^n$ is a Mori Dream Space then all the effective cones of cycles on $X_r^n$ are finitely generated.Comment: 26 pages; comments welcom

Algebraic K-theory of the first Morava K-theory

We compute the algebraic K-theory modulo p and v_1 of the S-algebra ell/p = k(1), using topological cyclic homology.Comment: Revised version, to appear in J. Eur. Math. Soc. (JEMS

Averting the Nazi Seizure of Power

The Great Depression in Germany led to the radicalization of the electorate, leading the country and then the world into the darkest days of Western Civilization. Could it have been otherwise? This paper explores whether the NSDAP takeover might have been averted with a fiscal policy that lowered the unemployment rate in those parts of Germany where their support rose most rapidly. A counterfactual simulation model based on estimates of the relationship between unemployment and the radical vote at the electoral district level provides a framework for considering how much lower unemployment would have to have been in those districts to prevent the NSDAP from becoming a formidable political force in Germany. Budget neutrality is maintained, so that the simulations do not depend on an expanded fiscal policy. The results indicate that such a policy could well have averted the NSDAP's seizure of power, and the catastrophe that followed in its wake