Related papers: Residue currents with prescribed annihilator ideal…

In this paper we introduce two new methods for constructing injective resolutions of sheaves of finite-dimensional vector spaces on finite posets. Our main result is the existence and uniqueness of a minimal injective resolution of a given…

Suppose that $X$ is an integral scheme (quasi-)projective over a complete local ring of mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a notion of a $+$-test ideal on $X$, including for divisors and…

The Fourier transform is considered as a Henstock--Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The…

We study the complete intersection property and the algebraic invariants (index of regularity, degree) of vanishing ideals on degenerate tori over finite fields. We establish a correspondence between vanishing ideals and toric ideals…

Let $(A,\m)$ be a \CM \ local ring with an infinite residue field and let $I$ be an $\m$-primary ideal. Let $\bx = x_1,\ldots,x_r$ be a $A$-superficial sequence \wrt \ $I$. Set $$\Vc_I(\bx) = \bigoplus_{n\geq 1} \frac{I^{n+1}\cap (\bx)}{\bx…

In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…

We generalize some properties related to Hilbert series and Lefschetz properties of Milnor algebras of projective hypersurfaces with isolated singularities to the more general case of an almost complete intersection ideal $J$ of dimension…

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional incompressible turbulence. The property we consider is selective decay, in which a…

Consider a grade 2 perfect ideal $I$ in $R=k[x_1,\cdots,x_d]$ which is generated by forms of the same degree. Assume that the presentation matrix $\varphi$ is almost linear, that is, all but the last column of $\varphi$ consist of entries…

For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents…

Results of Bohr-Neugebauer type are obtained for recurrent functions : If $y$ is a bounded uniformly continuous solution of a linear neutral difference-differential system with recurrent right-hand side, then $y$ is recurrent if $c_0 \not…

We study some fundamental properties of real rectifiable currents and give a generalization of King's theorem in characterizing currents defined by positive real holomorphic chains. Our proof uses Siu's semicontinuity theorem and largely…

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…

Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated…

Building on coprincipal mesoprimary decomposition [Kahle and Miller, 2014], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct…

Let S be a polynomial algebra over a field. If I is the edge ideal of a perfect semiregular tree, then we give precise formulas for values of depth, Stanley depth, projective dimension, regularity and Krull dimension of S/I.

We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms. These atoms are identified with the extreme points and…

We define a generalization of the winding number of a piecewise $C^1$ cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computation of this winding number relies on the Cauchy principal…

We develop a new method to study intersection theory of the main component of the Hilbert scheme of points on complex manifolds. The main result is an iterated residue formula for tautological integrals. We formulate a Chern-Segre-type…

The arithmetic rank of an ideal in a polynomial ring over an algebraically closed field is the smallest number of equations needed to define its vanishing locus set-theoretically. We determine the arithmetic rank of the generic $m$-residual…