An analytic construction of degenerating abelian varieties over complete rings
The topology of normal singularities of an algebraic surface and a criterion for simplicity
An analytic construction of degenerating curves over complete local rings
Theta characteristics of an algebraic curve
The Dawning of the Age of Stochasticity
For over two millennia, Aristotle's logic has ruled over the thinking of western intellectuals. All precise theories, all scientific models, even models of the process of thinking itself, have in principle conformed to the straight-jacket of logic. But from its shady beginnings devising gambling strategies and counting corpses in medieval London, probability theory and statistical inference now emerge as better foundations for scientific models, especially those of the process of thinking and as...
The irreducibility of the space of curves of given genus
On the Kodaira Dimension of the Moduli Space of Curves.
The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
Riemannian geometries on spaces of plane curves
We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms of , acting as reparametrizations. In particular we investigate the metric, for a constant , where is the curvature of the curve and , are normal vector fields to . The term is a sort of geometric Tikhonov regularization because, for , the geodesic distance between any two distinct curves is 0, while for the...
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms.
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