Related papers: Functorial monomialization and uniqueness of cente…
A functor of sets $\mathbb X$ over the category of $K$-commutative algebras is said to be an affine functor if its functor of functions, $\mathbb A_{\mathbb X}$, is reflexive and $\mathbb X=\Spec \mathbb A_{\mathbb X}$. We prove that affine…
We show that an everywhere regular foliation $\mathcal F$ with compact canonically polarized leaves on a quasi-projective manifold $X$ has isotrivial family of leaves when the orbifold base of this family is special. By a recent work of…
An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…
We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic resolution in characteristic zero, in the sense of Hironaka.…
In this paper we study some algebraic and combinatorial behaviors of expansion functor. We show that on monomial ideals some properties like polymatroidalness, weakly polymatroidalness and having linear quotients are preserved under taking…
The logarithm function is the gravitational potential in $\mathbb{R}^2$. We prove that the logarithm central force problem is block regularizable, that is, the (incomplete) flow may be continuously extended over the singularity at the…
Suppose that $f: Y\to X$ is a proper, dominant, tamely ramified morphism of algebraic surfaces, over a perfect field. We show that it is possible to perform sequences of monoidal transforms $Y'\to Y$ and $X'\to X$ to obtain an induced…
Let $\mathcal{L}$ be a finite-dimensional semisimple Lie algebra of rank $N$ over an algebraically closed field of characteristic $0$. Associated to $\mathcal{L}$ is a family of polynomial folding maps…
In the first chapter we present new results related on monomial ideals of Borel type. Also, we introduce a new class of monomial ideals, called $\de$-fixed ideals, which generalize the class of $p$-Borel ideals and we extend several results…
Let $h$ be a connective homology theory. We construct a functorial relative plus construction as a Bousfield localization functor in the category of maps of spaces. It allows us to associate to a pair $(X, H)$ consisting of a connected…
We study the behaviour of principal bundles under pullback along proper surjective morphisms of either schemes over an algebraically closed field of characteristic 0 or complex analytic spaces.
We construct a localization for operads with respect to one-ary operations based on the Dwyer-Kan hammock localization. For an operad O and a sub-monoid of one-ary operations W we associate an operad LO and a canonical map O to LO which…
Birational properites of generically finite morphisms $X\rightarrow Y$ of algebraic varieties can be understood locally by a valuation of the function field of $X$. In finite extensions of algebraic local rings in characteristic zero…
In this paper we use polarization to study the behavior of the depth and regularity of a monomial ideal $I$, locally at a variable $x_i$, when we lower the degree of all the highest powers of the variable $x_i$ occurring in the minimal…
We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are…
We investigate relative cohomology functors on subcategories of abelian categories via Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that certain comparison maps between these functors are isomorphisms…
For a conformal vector field on a closed, real-analytic, Lorentzian manifold we prove that the flow is locally isometric -- that it preserves a metric in the conformal class on a neighborhood of any point -- or the metric is everywhere…
When studying local properties of a polynomial ideal, one usually needs a theoretic technique called localization. For most cases, in spite of its importance, the computation in a localized ring cannot be algorithmically preformed. On the…
For a finite group $D$, we study categorical factorisation homology on oriented surfaces equipped with principal $D$-bundles, which `integrates' a (linear) balanced braided category $\mathcal{A}$ with $D$-action over those surfaces. For…
Our main result is the following: let X be a normal affine toric surface without torus factor. Then there exists a non-normal affine toric surface X' with automorphism group isomorphic to the automorphism group of X if and only if X is…