A universal magnification theorem. II. Generic caustics up to codimension five

A Codimension Theorem for Complete Toric Varieties

Let X be a complete toric variety with homogeneous coordinate ring S. In this article, we study the codimension in the critical degree of ideals of S generated by dim(X) + 1 homogeneous elements that don’t vanish simultaneously on X. Introduction In this paper, X will denote a complete toric variety of dimension n. We will work over C, so that the torus of X is (C). The dual lattices will be de...

Forbidden magnification? II

The twin of this paper, “Forbidden Magnification? I.” [1], presents systematic SOM simulations with the explicit magnification control scheme of Bauer, Der, and Herrmann [2] on data for which the theory does not guarantee success, namely data that are n-D, n > 2 and/or data whose components in the different dimensions are not statistically independent. For the unsupported n = 2 cases that we in...

Unirational threefolds with no universal codimension cycle

Weprove that the general quartic double solidwith k ≤ 7 nodes does not admit a Chow theoretic decomposition of the diagonal, (or equivalently has a nontrivial universal CH0 group,) and the same holds if we replace in this statement “Chow theoretic” by “cohomological”. In particular, it is not stably rational. We also deduce that the general quartic double solid with seven nodes does not admit a...

Generation of the Ahlfors Five Islands Theorem

A Generic Cyclic Theorem Prover

We describe the design and implementation of an automated theorem prover realising a fully general notion of cyclic proof. Our tool, called Cyclist, is able to construct proofs obeying a very general cycle scheme in which leaves may be linked to any other matching node in the proof, and to verify the general, global infinitary condition on such proof objects ensuring their soundness. Cyclist is...