Related papers: Almost set-theoretic complete intersections in cha…

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…

Let K be an algebraically closed field of characteristic zero. We show that if the automorphisms group of a quasi-affine variety X is infinite, then X is uniruled.

Let $G=(V,E)$ be a finite, simple graph. We consider for each oriented graph $G_{\cal O}$ associated to an orientation ${\cal O}$ of the edges of $G$, the toric ideal $P_{G_{\cal O}}$. In this paper we study those graphs with the property…

We characterize those valued fields for which the image of the valuation ring under every polynomial in several variables contains an element of maximal value, or zero.

Let V be a variety of algebras of some type. An interest to describing automorphisms of the category C of finitely generated free V-algebras was inspired in connection with development of universal algebraic geometry founded by B. Plotkin.…

Let $A$ denote an affine algebra over an algebraically closed field $k$, with $\dim A=d\geq 3$. In the light of availability of cancellation theorems for stably free modules $P$ with $rank(P)=d-1$ (corank one), we try to implement the…

I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian…

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$ of prime characteristic. We describe the intersection of a subvariety $X$ of $G$ with a finitely generated subgroup of $G(K)$.

In this paper we classify the unimodal isolated complete intersection singularities in arbitrary characteristic under contact equivalence. The classification over $\mathbb{C}$ has already done by A. Dimca and C.G. Gibson. We continue and…

We characterize the limit periodic sets of families of polynomial planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere with…

In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…

For a class V of algebras, denote by Conc(V) the class of all semilattices isomorphic to the semilattice Conc(A) of all compact congruences of A, for some A in V. For classes V1 and V2 of algebras, we denote by crit(V1,V2) the smallest…

For an arbitrary field K, let I be an ideal in the ring K[[x,y]] expressible as a polynomial in either the pair of ideals (x, y^4) and (x,y) or the pair (x,y^3) and (x^2, y). Let G be the group of automorphisms of K[[x,y]] sending the ideal…

We prove that up to automorphisms a line admits a unique embedding into the regular part of of a simplicial toric variety of dimension n>=4 over an algebraically closed field of characteristic zero which is smooth in codimension 2.

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It…

A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent to a variety. This is quite analogous to Lawvere's classical…

We generalize Givental's Theorem for complete intersections in smooth toric varieties in the Fano case. In particular, we find Gromov--Witten invariants of Fano varieties of dimension $\geq 3$, which are complete intersections in weighted…

We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties in any characteristic, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to…

The K-rings of non-singular complex pro jective varieties as well as quasi- toric manifolds were described in terms of generators and relations in an earlier work of the author with V. Uma. In this paper we obtain a similar description for…

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…