On the frequency of algebraic Brauer classes on certain log K3 surfaces

Given systems of two (inhomogeneous) quadratic equations in four variables, it is known that the Hasse principle for integral points may fail. Sometimes this failure can be explained by some integral Brauer-Manin obstruction. We study the existence of a non-trivial algebraic part of the Brauer group for a family of such systems and show that the failure of the integral Hasse principle due to an algebraic Brauer-Manin obstruction is rare, as for a generic choice of a system the algebraic part of the Brauer-group is trivial. We use resolvent constructions to give quantitative upper bounds on the number of exceptions.Comment: 13 page

On the Brauer-Manin obstruction for degree four del Pezzo surfaces

We show that, for every integer $1 \leq d \leq 4$ and every finite set $S$ of places, there exists a degree $d$ del Pezzo surface $X$ over ${\mathbb Q}$ such that ${\rm Br}(X)/{\rm Br}({\mathbb Q}) \cong {\mathbb Z}/2{\mathbb Z}$ and the Brauer-Manin obstruction works exactly at the places in $S$. For $d = 4$, we prove that in all cases, with the exception of $S = \{\infty\}$, this surface may be chosen diagonalizably over ${\mathbb Q}$

On the number of certain Del Pezzo surfaces of degree four violating the Hasse principle

We give an asymptotic expansion for the density of del Pezzo surfaces of degree four in a certain Birch Swinnerton-Dyer family violating the Hasse principle due to a Brauer-Manin obstruction. Under the assumption of Schinzel's hypothesis and the finiteness of Tate-Shafarevich groups for elliptic curves, we obtain an asymptotic formula for the number of all del Pezzo surfaces in the family, which violate the Hasse principle.Comment: 27 page

On the algebraic Brauer classes on open degree four del Pezzo surfaces

We study the algebraic Brauer classes on open del Pezzo surfaces of degree $4$. I.e., on the complements of geometrically irreducible hyperplane sections of del Pezzo surfaces of degree $4$. We show that the $2$-torsion part is generated by classes of two different types. Moreover, there are two types of $4$-torsion classes. For each type, we discuss methods for the evaluation of such a class at a rational point over a $p$-adic field

Symbolic struggles over solidarity in times of crisis: trade unions, civil society actors and the political far right in Austria

As a consequence of the recent financial and economic crisis, social cohesion and integration are in jeopardy all over Europe. In this context, scholars also speak of decreasing solidarity, which is defined as a normative obligation to help each other and to make sacrifices to reach common goals. By taking the empirical example of Austria, we argue that the meaning of solidarity is increasingly being contested. Various collective actors such as trade unions, civil society actors, but also right-wing populist parties are engaged in symbolic struggles over solidarity. To show this, we examine the different concepts and foundations of solidarity and analyse where and why they conflict with each other, referring to recent debates on political issues, such as the needs-based minimum benefit system and the access to the labour market for refugees

Del Pezzo surfaces of degree four violating the Hasse principle are Zariski dense in the moduli scheme

We show that, over every number field, the degree four del Pezzo surfaces that violate the Hasse principle are Zariski dense in the moduli scheme.Comment: 21 page