Extensions of complex varieties across $C^1$ manifolds.

Neighborhoods of Analytic Varieties in Complex Manifolds

Extensions of Toric Varieties

In this paper, we introduce the notion of “extension” of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or arithmetically Cohen-Macaulay (Gorenstein) and having a Cohen-Macaulay tangent cone or a local ring with non-decreasing Hilbert function, from just one singl...

Cyclic Extensions of Order Varieties

It is known that the problem of telling whether a cyclic order is included in some cycle is NP-complete. We show that the same question for order varieties, a special class of cyclic orders, is in L. For this, we relate the entropy relation between partial orders to the forcing relation of graph theory.

Central Extensions in Mal’tsev Varieties

We show that every algebraically–central extension in a Mal’tsev variety — that is, every surjective homomorphism f : A−→ B whose kernel–congruence is contained in the centre of A, as defined using the theory of commutators — is also a central extension in the sense of categorical Galois theory; this was previously known only for varieties of Ω-groups, while its converse is easily seen to hold ...

The Fbi Transform on Compact C1 Manifolds