Related papers: Finite Generation of Canonical Rings

We prove that a finite-dimensional omega-categorical group is finite-by-abelian-by-finite and that a finite-dimensional omega-categorical ring is virtually finite-by-null.

We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.

We study the anti-canonical ring of a projective variety and we characterise varieties of log Fano type depending on the singularities of these models.

We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.

We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure.

For a commutative ring R we investigate the property that the sets of minimal primes of finitely generated ideals of R is always finite. We prove this property passes to polynomial ring extensions (in an arbitrary number of variables) over…

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…

Over a field of prime characteristic $p>2$, we prove that the cohomology rings of some pointed Hopf algebras of dimension $p^3$ are finitely generated. These are Hopf algebras arising in the ongoing classification of finite dimensional Hopf…

Let $(G_n,X_n)$ be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated permutational wreath product $...\wr G_2\wr G_1$ is topologically finitely generated if…

We construct affine spaces, projective spaces and grassmannians in the ca\-te\-gory of ringed spaces. We show how finite posets and sheaves of rings on them appear in a natural way.

We prove the termination of 4-fold canonical flips.

We consider codes defined over an affine algebra $\mathcal A=R[X_1,\dots,X_r]/\left\langle t_1(X_1),\dots,t_r(X_r)\right\rangle$, where $t_i(X_i)$ is a monic univariate polynomial over a finite commutative chain ring $R$. Namely, we study…

We study projective manifolds with nonamenable and non-residually finite fundamental groups. We generalize the uniformization theorem of our earlier note. We generalize a classical theorem of Maltsev about finitely generated subgroups of…

We introduce the finitistic extension degree of a ring and investigate rings for which it is finite. The Auslander-Reiten Conjecture is proved for rings of finite finitistic extension degree and these rings are also shown to have finite…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

We prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…

We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is finite, and that this number is uniformly bounded in any finite type family of base varieties. As a…

The main aim of this paper is to investigate rings over which all (finitely generated strongly) Gorenstein projective modules are projective. We consider this propriety under change of rings, and give various examples of rings with and…

Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…

We prove that the derived categories for toric varieties have complete exceptional collections.