On non-rigid del Pezzo fibrations of low degree

We consider $\mathbb{P}(1,1,1,2)$ bundles over $\mathbb{P}^1$ and construct hypersurfaces of these bundles which form a degree 2 del Pezzo fibration over $\mathbb{P}^1$ as a Mori fibre space. We classify all such hypersurfaces whose type \III or \IV Sarkisov links pass to a different Mori fibre space. A similar result for cubic surface fibrations over $\mathbb{P}^2$ is also presented.Comment: 34 page

Acts of the State and Representation in Edith Stein

This paper discusses the thesis defended by Edith Stein that certain acts can be attributed to the State. According to Stein, the State is a social structure characterized by sovereignty. As such, it is responsible for the production, interpretation, and application of law. These tasks require the performance of acts, most of which are what Stein calls “social acts” like enactments and orders. For Stein, the acts in question are made by the organs of the State, but in the name of the State, and are thus attributed to the State via a relation of representation. In the first section, the paper presents Stein’s thesis that the sovereignty of the State entails a series of legal prerogatives, which in turn result in various social acts being ascribed to the State through its representatives. In the second section, the paper critically discusses Stein’s views, notably her theory of representation, and her account of the nature of the State, while emphasizing its most interesting aspects, namely, its fine-grained analyses of the various acts that are attributed to the State

Kant’s Antinomy of Teleology: In Defense of a Traditional Interpretation

Kant’s Antinomy of Teleological Judgment is unique in offering two pairs of oppositions, one of regulative maxims, and the other of constitutive principles. Here I defend a traditional interpretation of the antinomy— as proposed, for example, by Stadler (1874), Adickes (1925), and Cassirer (1921)—that the antinomy consists in an opposition between constitutive principles, and is resolved by pointing out their legitimate status as merely regulative maxims. I argue against recent interpretations—for example, in McLaughlin (1990), Allison (1991), and Watkins (2009)—which treat the regulative pair as itself antinomial. I then address several textual worries having to do with reconciling the traditional interpretation within the overall structure of the Dialectic of Teleological Judgment that have led these scholars to espouse the new view. Throughout the paper, I emphasize hitherto neglected parallels with Kant’s treatment of the antinomy of taste, which sheds light on understanding the antinomy of teleology