Related papers: Analysis on some infinite modules, inner projectio…

Given a standard graded polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic zero and a graded $k$-subalgebra $A=k[f_1,...,f_m]\subset R$, one relates the module $\Omega_{A/k}$ of K\"ahler $k$-differentials of $A$ to the…

The quasi-projective dimension and quasi-injective dimension are recently introduced homological invariants that generalize the classical notions of projective dimension and injective dimension, respectively. For a local ring $R$ and…

Let $X= \mathbb{P}^1 \setminus \{0,1,\infty\}$, and let $S$ denote a finite set of prime numbers. In an article of 2005, Minhyong Kim gave a new proof of Siegel's theorem for $X$: the set $X(\mathbb{Z}[S^{-1}])$ of $S$-integral points of…

Given an algebraically closed field $K$ of characteristic zero, we study the incidence relation between points and irreducible projective curves, or more precisely the poset of irreducible proper subvarieties of $\mathbb P^2(K)$. Answering…

Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…

We define and study the metric, or extreme version of the notion of a projective normed module. The relevant definition takes into account the exact value of the norm of the module in question, in contrast with the standard known definition…

Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…

We investigate homological and depth-theoretic properties of finitely generated modules of finite projective dimension over Noetherian local rings. A central theme is the study of criteria for freeness and reflexivity derived from the…

In this article we continue our investigation of the Derived Equivalences over noetherian quasi-projective schemes $X$, over affine schemes $\spec{A}$. For integers $k\geq 0$, let $C{\mathbb M}^k(X)$ denote the category of coherent…

The metric projection onto the positive semidefinite (PSD) cone is strongly semismooth, a property that guarantees local quadratic convergence for many powerful algorithms in semidefinite programming. In this paper, we investigate whether…

Persistence modules serve as the algebraic foundation for topological data analysis, typically studied as representations of posets over a field. This article extends the structural and decomposition theory of persistence modules to the…

This paper studies the asymptotic behavior of the syzygies of a smooth projective variety X as the positivity of the embedding line bundle grows. We prove that as least as far as grading is concerned, the minimal resolution of the ideal of…

Let $R$ be a fibre product of standard graded algebras over a field. We study the structure of syzygies of finitely generated graded $R$-modules. As an application of this, we show that the existence of an $R$-module of finite regularity…

Jacob Lurie (arXiv:math/0412266) has shown that for geometric stacks X,Y every cocontinuous tensor functor F : Qcoh(X) -> Qcoh(Y) is the pullback of a morphism Y -> X under the additional assumption that F is tame. In this note we get rid…

We study Lagrangian embeddings of a class of two-dimensional cell complexes $L_{p,q}$ into the complex projective plane. These cell complexes, which we call pinwheels, arise naturally in algebraic geometry as vanishing cycles for quotient…

We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a…

Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a…

Spline functions are smooth piecewise polynomials widely used for interpolation and smoothing, and nonnegative spline smoothing is also studied for nonnegative data. Previous research used sufficient conditions for the nonnegativity of…

It is proved that, for a left hereditary ring, an arbitrary left module has a representation in the form of the direct sum of a stable left module and indecomposable projective left modules (if and only if an arbitrary left module has a…

We prove an elementary but somewhat unexpected result about projective embeddings of smooth varieties X whose cotangent bundles are numerically effective. Specifically, we show that the degree of X in any projective embedding must grow…