3 papers
math.AG2026
Automorphisms of toric varieties and Gale duality
Ivan Arzhantsev, Kirill Shakhmatov
We classify complete toric threefolds such that the automorphism group acts on with an open orbit whose complement does not contain a divisor. The latter co…
math.AG2026
Cylinders and the zero locus of the plinth ideal
Kirill Shakhmatov
Given a -action on an affine variety , we show that the complement of the union of all principal invariant cylinders in is equal to the zero locus of…
math.AG2025
On flexibility of affine factorial varieties
Ivan Arzhantsev, Kirill Shakhmatov
We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine fact…