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Related papers: An effective uniform Artin-Rees lemma

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We give a principle in derived categories, which lies behind the classical Auslander-Reiten duality and its generalized version by Iyama and Wemyss. We apply the principle to show the validity of the Auslander-Reiten conjecture over a…

Commutative Algebra · Mathematics 2018-05-16 Maiko Ono , Yuji Yoshino

We prove that every irreducible component of semi-regular loci of effective line bundles in the Picard scheme of a smooth projective variety has at worst rational singularities. This generalizes Kempf's result on rational singularities of…

Algebraic Geometry · Mathematics 2014-09-30 Lei Song

By a [$K$-]approximate subring of a ring we mean an additively symmetric subset $X$ such that $X \cdot X \cup (X + X)$ is covered by finitely many [resp.\ $K$] additive translates of $X$. We prove a structure theorem for finite approximate…

Rings and Algebras · Mathematics 2026-04-07 Krzysztof Krupiński , Simon Machado

We prove a version of Linnik's basic lemma uniformly over the base field using theta-series and geometric invariant theory in the spirit of Khayutin's approach (Duke Math. J., 168(12), 2019). As an application, we establish entropy bounds…

Number Theory · Mathematics 2025-08-05 Andreas Wieser , Pengyu Yang

The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The…

Commutative Algebra · Mathematics 2026-03-03 Sara Kališnik , Davorin Lešnik

We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We…

Algebraic Geometry · Mathematics 2021-03-09 Niels Lubbes

Let $X$ be any smooth simply connected projective surface. We consider some moduli space of pure sheaves of dimension one on $X$, i.e. $\mhu$ with $u=(0,L,\chi(u)=0)$ and $L$ an effective line bundle on $X$, together with a series of…

Algebraic Geometry · Mathematics 2012-06-22 Yao Yuan

We give a short proof of the Gauss-Bonnet theorem for a real oriented Riemannian vector bundle $E$ of even rank over a closed compact orientable manifold $M$. This theorem reduces to the classical Gauss-Bonnet-Chern theorem in the special…

Differential Geometry · Mathematics 2007-05-23 Denis Bell

We introduce a theory of uniform K-stability for big line bundles on smooth projective varieties. This extends the existing theory both for varieties with ample line bundles, and for varieties with big anticanonical class. Our main result…

Algebraic Geometry · Mathematics 2026-03-27 Ruadhaí Dervan , Rémi Reboulet

We give the theorem of coincidence of a class of functions defined by a generalised modulus of smoothness with a class of functions defined by the order of the best approximation by algebraic polynomials. We also prove the appropriate…

Functional Analysis · Mathematics 2012-08-28 Faton M. Berisha

A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…

Combinatorics · Mathematics 2026-05-26 Guy Moshkovitz , Dora Woodruff

We prove a high order Schwarz-Pick lemma for mappings between unit balls in complex spaces in terms of the Bergman metric. From this lemma, Schwarz-Pick estimates for partial derivatives of arbitrary order of mappings are deduced.

Complex Variables · Mathematics 2011-09-14 Shaoyu Dai , Huaihui Chen , Yifei Pan

We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is stratifed according to genus, and it carries a metric and a measure that…

Algebraic Geometry · Mathematics 2017-02-01 Lizhen Ji , Juergen Jost

We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…

Commutative Algebra · Mathematics 2008-06-04 Kei-ichiro Iima , Yuji Yoshino

A relative Picard theory in the context of graded manifolds is introduced. A Berezinian calculus and a theory of connections over SUSY-curves are systematically developed, and used to prove a Gauss-Bonnet theorem for line bundles in that…

High Energy Physics - Theory · Physics 2009-10-22 U. Bruzzo , J. A. Dominguez Perez

We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower and upper bounds for the number of rational points of a…

Number Theory · Mathematics 2024-06-04 Martin Hils , Ehud Hrushovski , Jinhe Ye , Tingxiang Zou

Let $X$ be a smooth projective variety defined over a number field $K$. We give an upper bound for the generalized greatest common divisor of a point $x\in X$ with respect to an irreducible subvariety $Y\subseteq X$ also defined over $K$.…

Number Theory · Mathematics 2024-11-12 Benjamín Barrios

We apply the supergeometric analogue of Artin's algebraicity criteria to prove algebraicity for four moduli problems in supergeometry: supercurves, super Riemann surfaces, stable supercurves, and stable super Riemann surfaces. The…

Algebraic Geometry · Mathematics 2026-03-18 Nadia Ott

We prove an index theorem for the quotient module of a monomial ideal. We obtain this result by resolving the monomial ideal by a sequence of Bergman space like essentially normal Hilbert modules.

Operator Algebras · Mathematics 2017-08-22 Ronald G. Douglas , Mohammad Jabbari , Xiang Tang , Guoliang Yu

In this note, we consider a situation that is generally used as an intermediate technical step in proving the Artin-Rees lemma but otherwise is not much discussed in introductory accounts of commutative algebra. I hope to show in this note…

Commutative Algebra · Mathematics 2017-09-27 Nicholas Phat Nguyen