Related papers: Monomial resolutions of morphisms of algebraic sur…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…

We construct comparison morphisms between two well-known projective resolutions of a monomial algebra $A$: the bar resolution and Bardzell's resolution; the first one is used to define the cup product and the Lie bracket on the Hochschild…

We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their…

In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism admits a lifting to these quotient presentations. We show that…

For any genuinely ramified morphism $f\, :\, Y\, \longrightarrow\, X$ between irreducible smooth projective curves we prove that $\overline{(Y\times_X Y) \setminus \Delta}$ is connected, where $\Delta\, \subset\, Y\times_X Y$ is the…

We first show that any connected algebraic group over a perfect field is the neutral component of the automorphism group scheme of some normal projective variety. Then we show that very few connected algebraic semigroups can be realized as…

For a symplectic geometry $X$, suppose the (derived) Fukaya category $\mathrm{Fuk}(X)$ of $X$ is equipped with a monoidal structure. Then its Balmer spectrum recovers a mirror $Y$ of $X$ if there exists homological mirror symmetry…

We prove that a birational morphism of projective 3-folds, over a field of characteristic zero, can be made toroidal by performing a sequence of blow ups of points and nonsingular curves above the domain and target.

We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic…

We study equivariant morphisms from zero dimensional schemes to varieties and show that, under suitable assumptions, all such morphisms factor via a canonical one. We relate the above to Algebraic Representations of Ergodic Actions.

Let $X,Y$ be two irreducible subvarieties of the projective space $\mathbb{P}^n$, and $d\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\bf explicitly}, in terms of $d$ and the ideals defining $X$ and…

We show that every finitely generated conical refinement monoid can be represented as the monoid $\mathcal V(R)$ of isomorphism classes of finitely generated projective modules over a von Neumann regular ring $R$. To this end, we use the…

We present a complete classification of complex projective surfaces $X$ with nontrivial self-maps (i.e. surjective morphisms $f:X\rightarrow X$ which are not isomorphisms) of any given degree. The starting point of our classification are…

There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring. The definition involves Gr\"obner bases or the action of an algebraic torus. We present algorithms for computing the (affine schemes…

We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection…

Let $\mathbb F$ be an algebraically closed field, $G$ be an abelian group, and let $A$ and $B$ be arbitrary finite-dimensional $G$-graded simple algebras over $\mathbb F$. We prove that $A$ and $B$ are isomorphic if, and only if, they…

Let $Y$ be a normal and projective variety over an algebraically closed field $k$ and $V$ a vector bundle over $Y$. We prove that if there exist a $k$-scheme $X$ and a finite surjective morphism $g:X\to Y$ that trivializes $V$ then $V$ is…

The space of monic squarefree complex polynomials has a stratification according to the multiplicities of the critical points. We introduce a method to study these strata by way of the infinite-area translation surface associated to the…

We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…

Let $A$ be a finite dimensional algebra having the double centraliser property with respect to a minimal faithful projective-injective left module $Af$ for some idempotent $f$. We prove that in this case $A$ is a monomial algebra if and…