Invariant deformation theory of affine schemes with reductive group action

We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we device an algorithm to compute the universal deformation of $X$ in terms of generators and relations up to a given order. In many situations, our algorithm even computes an algebraization of the universal deformation. As an application, we determine new families of examples of the invariant Hilbert scheme of Alexeev and Brion, where $G$ is a classical group acting on a classical representation, and describe their singularities.Comment: 43 pages, final version, to appear in J. Pure Appl. Algebr

The global moduli theory of symplectic varieties

We develop the global moduli theory of symplectic varieties {in the sense of Beauville}. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of Verbitsky's global Torelli theorem in the smooth case (assuming $b_2\geq 5$) which does not use the existence of a hyperk\"ahler metric or twistor deformations.Comment: Some rearrangements, simplifications, and minor corrections. Comments welcome

Footnotes to the birational geometry of primitive symplectic varieties

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.Comment: Final version. To appear in "Perspectives on four decades. Algebraic Geometry 1980 - 2020. In memory of Alberto Collino". Trends in Mathematics. Birkhause

Interaction and interactives: collaboration and participation with computer-based exhibits

It is increasingly recognized that social interaction and collaboration are critical to our experience of museums and galleries. Curators, museum managers and designers are exploring ways of enhancing interaction and in particular using tools and technologies to create new forms of participation, with and around, exhibits. It is found, however, that these new tools and technologies, whilst enhancing “interactivity,” can do so at the cost of social interaction and collaboration, inadvertently impoverishing co-participation, and cooperation. In this paper we address some of the issues and difficulties that arise in designing for “interactivity” and in particular point to the complex and highly contingent forms of social interaction which arise with, and around, exhibits. The paper is based on a series of video-based field studies of conduct and interaction in various museums and galleries in London and elsewhere including the Science Museum and Explore@Bristol