Related papers: A Proof of Desingularization over fields of charac…

A class of desingularizations for orbit closures of representations of Dynkin quivers is constructed, which can be viewed as a graded analogue of the Springer resolution. A stratification of the singular fibres is introduced; its geometry…

Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…

We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees smoothness on the Hilbert scheme. Moreover, we conjecture…

This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a…

We study the algebraic $K$-theory of smooth schemes over $W_n(\Bbbk)$, where $\Bbbk$ is a perfect field of characteristic $p>0$. For a $p$-adic smooth scheme $X_{\centerdot}$ over $W_{\centerdot}(k)$, we introduce complexes…

Let $M$ be the circle or a compact interval, and let $\alpha=k+\tau\ge1$ be a real number such that $k=\lfloor \alpha\rfloor$. We write $\mathrm{Diff}_+^{\alpha}(M)$ for the group of $C^k$ diffeomorphisms of $M$ whose $k^{th}$ derivatives…

Let $(A,B)$ be a pair of skew-symmetric matrices over a field of characteristic not 2. Its regularization decomposition is a direct sum \[ (\underline{\underline A},\underline{\underline B})\oplus (A_1,B_1)\oplus\dots\oplus(A_t,B_t) \] that…

Let $W$ be a compact smooth $4$-manifold that deformation retract to a PL embedded closed surface. One can arrange the embedding to have at most one non-locally-flat point, and near the point the topology of the embedding is encoded in the…

We present a classification algorithm for isolated hypersurface singularities of corank 2 and modality 1 over the real numbers. For a singularity given by a polynomial over the rationals, the algorithm determines its right equivalence class…

An explicit computation of the so-called string-theoretic E-function of a normal complex variety X with at most log-terminal singularities can be achieved by constructing one snc-desingularization of X, accompanied with the intersection…

Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…

We give a constructive proof that $R[X]$ is normal when $R$ is normal. We apply this result to an operation needed for studying the henselization of a local ring. Our proof is based on the case where $R$ is without zero divisors, which is…

Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced…

We provide a new proof of the following result: Let $X$ be a variety of finite type over an algebraically closed field $k$ of characteristic 0, let $Z\subset X$ be a proper closed subset. There exists a modification $f:X_1 \rar X$, such…

Let $M$ be strongly minimal and constructed by a `Hrushovski construction'. If the Hrushovski algebraization function $\mu$ is in a certain class ${\mathcal T}$ ($\mu$ triples) we show that for independent $I$ with $|I| >1$, ${\rm…

We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces, whose components intersect in a transversal way but may be themselves singular. Such hypersurfaces will be called…

For proper morphisms, we give a functorial flatification algorithm by blow-ups in the spirit of Hironaka's flatification algorithm. In characteristic zero, this gives functorial flatification by blow-ups in smooth centers. We also give a…

In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone r-by-s matrices. These algorithms can be used, for…

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

To, say, a proper algebraic or holomorphic space $X/S$, and a coherent sheaf ${\mathcal F}$ on $X$ we identify a functorial ideal, the fitted flatifier, blowing up sequentially in which leads to a flattening of the proper transform of…