Nagata Compactification for Algebraic Spaces

Topology Proceedings 2 (1977) pp. 169-178: AN ALGEBRAIC CHARACTERIZATION OF THE FREUDENTHAL COMPACTIFICATION FOR A CLASS OF RIMCOMPACT SPACES

Embedding measure spaces

‎For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable‎. ‎The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space‎. ‎Under certain conditions the construction simplifies‎. ‎Examples are given when this simplification o...

On some causal and conformal groups

We determine the causal transformations of a class of causal symmetric spaces (Th. 2.4.1). As a basic tool we use causal imbeddings of these spaces as open orbits in the conformal compactification of Euclidean Jordan algebras. In the first chapter we give elementary constructions of such imbeddings for the classical matrix-algebras. In the second chapter we generalize these constructions for ar...

Twistor Lines on Nagata Threefold

We present an explicit description of twistor lines in M. Nagata’s example of nonprojective complete algebraic variety and give a direct proof of the fact that Nagata’s example is a compactification of the twistor space of a hyperKähler metric on the cotangent bundle of P . We particularly observe that there exists a pair of 4-dimensional families of real lines and that precisely one of these f...

Algebraic and tropical curves: comparing their moduli spaces

We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its bordification given by weighted tropical curves, and its compactification by extended (weighted) tropical curves. We compare it to the moduli spaces of smooth and stable, n-pointed algebraic curves, from the combinatorial, the topological, and the Teichmüller point of view.