Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n-1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}-actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}-actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).

Flexible varieties and automorphism groups

Given an irreducible affine algebraic variety X of dimension n≥2 , we let SAut(X) denote the special automorphism group of X , that is, the subgroup of the full automorphism group Aut(X) generated by all one-parameter unipotent subgroups. We show that if SAut(X) is transitive on the smooth locus X reg , then it is infinitely transitive on X reg . In turn, the transitivity is equivalent to the flexibility of X . The latter means that for every smooth point x∈X reg the tangent space T x X is spanned by the velocity vectors at x of one-parameter unipotent subgroups of Aut(X) . We also provide various modifications and applications.

Theories of Militancy in Practice: Explanations of Muslim Terrorism in India

This article analyzes the interaction between theories of radicalization and state responses to militancy in India. Focusing on the interpretation of the increased frequency of terrorist attacks in Indian metropolises in the last decade, the article examines the narratives surrounding those classified as terrorists in the context of rising Muslim militancy in the country. Different state agencies operate with different theories about the links between processes of radicalization and terrorist violence. The scenarios of radicalization underlying legislative efforts to prevent terrorism, the construction of motives by the police, and the interpretation of violence by the judiciary all rely on assumptions about radicalization and violence. Such narratives are used to explain terrorism both to security agencies and to the public; they inform the categories and scenarios of prevention. Prevention relies on detection of future deeds, planning, intentions, and even potential intentions. "Detection" of potential intentions relies on assumptions about specific dispositions. Identification of such dispositions in turn relies on the context-specific theories of the causes of militancy. These determine what "characteristics" of individuals or groups indicate potential threats and form the basis for their categorization as "potentially dangerous." The article explores the cultural contexts of theories of radicalization, focusing on how they are framed by societal understandings of the causes of deviance and the relation between the individual and society emerging in contemporary India. It examines the shift in the perception of threat and the categories of "dangerous others" from a focus on role to a focus on ascriptive identity.