A natural question is to determine which algebraic stacks are quotient stacks. In this paper we give some partial answers and relate it the of whether, for a scheme X, map from Brauer group (equivalence classes Azumaya algebras) cohomological (the torsion subgroup H 2 ( X , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] m )) surjective.

We prove the localization theorem for torus actions in equivariant intersection theory. Using we give another proof of Bott residue formula Chern numbers bundles on smooth complete varieties. In addition, our techniques allow us to obtain formulas a certain class singular schemes which admit actions. This is rather special, but it includes some interesting examples such as intersections and Schubert

The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with action a linear group $G$. For $G$-space $X$, gives isomorphism between completion the Grothendieck and Chow groups. The key proving geometric description completions group. Besides Riemann-Roch, result has some purely $K$-theoretic applications. In particular, we conjecture K\ock (in case regular schemes) extend arbitrary characteristic Segal on representation rings.

We study the ring of characteristic classes with values in Chow for principal $G$-bundles over schemes. If we consider bundles which are locally trivial Zariski topology, then show, $G$ reductive, that this is isomorphic to Weyl group invariants algebra generated by characters maximal torus. For general same isomorphism holds after tensoring coefficients ${\Bbb Q}$. As a corollary, show any (non-torsion) topological class algebraic when applied complex varieties.

In this paper we establish a surprising new identity for Parseval frames in Hilbert space. Several variations of result are given, including an extension to general frames. Finally, discuss the derived results.

In this paper we construct Stiefel-Whitney and Euler classes in Chow cohomology for algebraic vector bundles with nondegenerate quadratic form. These are not the algebra generated by Chern of such new characteristic geometry. On complex varieties, they correspond to same name pulled back from classifying space BSO(N,C). The only geometry coming classical groups ([T2], [EG]). We begin using quadric study maximal isotropic subbundles. If V → X is a bundle form, if E F subbundles then prove...

The objective of this paper is the linear reconstruction a vector, up to unimodular constant, when all phase information lost, meaning only magnitudes frame coefficients are known. Reconstruction algorithms type relevant for several areas signal communications, including wireless and fiber-optical transmissions. discussed here rely on suitable rank-one operator valued frames defined finite-dimensional real or complex Hilbert spaces. Examples such operator-valued Hermitian operators...

The problem of recovering a pair signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In this paper, we prove that order to determine generic uniquely, up trivial ambiguities, the number one needs collect is, at most, five times parameters required describe signals. This result improves significantly upon previous papers, which be quadratic rather...

The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends to compact groups, addressing recovery of set matrices their Gram matrices. In this broader context, missing phases in space are replaced unitary or orthogonal arising action group on finite-dimensional vector space. generalization is driven applications multi-reference alignment and single-particle...

We construct new classes of Parseval frames for a Hilbert space which allow signal reconstruction from the absolute value frame coefficients. As consequence, can be done without using noisy phase or its estimation. This verifies longstanding conjecture speech processing community.

The purpose of this letter is to prove, for real frames, that signal reconstruction from the absolute value frame coefficients equivalent solution a sparse optimization problem, namely minimum lscr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sup> (quasi)norm over linear constraint. This constraint reflects relationship within range analysis operator

Let g be an even positive integer.In this paper we compute the integral Chow ring of stack smooth hyperelliptic curves genus g.

We study the dihedral multi-reference alignment problem of estimating orbit a signal from multiple noisy observations signal, acted on by random elements group. show that if group are drawn generic distribution, is uniquely determined second moment observations. This implies optimal estimation rate in high noise regime proportional to square variance noise. first result this type for over non-abelian with non-uniform distribution elements. Based tools invariant theory and algebraic geometry,...

We derive fast algorithms for doing signal reconstruction without phase. This type of problem is important in processing, especially speech recognition technology, and has relevance state tomography quantum theory. show that a generic frame gives from the absolute value coefficients polynomial time. An improved efficiency obtained with family sparse frames or associated complex projective 2-designs.

We give a purely equivariant construction of orbifold products for quotient Deligne-Mumford stacks [X/G] where G is an arbitrary linear algebraic group (not necessarily finite). The key to our the definition "logarithmic trace" vector bundle. also prove that there Chern character homomorphism which induces isomorphism canonical summand in Grothendieck ring with Chow ring. As application we obtain associative product on (as opposed its inerita stack) taken complex coefficients.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 24 February 2020Accepted: 14 July 2020Published online: 15 September 2020Keywordsphase retrieval, X-ray crystallography, sparsity, symmetry groupAMS Subject Headings94A12, 15A29, 15A63, 13P25Publication DataISSN (online): 2577-0187Publisher: Society for Industrial and Applied MathematicsCODEN: sjmdaq

In this expository article we give a categorical definition of the integral cohomology ring stack. We show that for quotient stacks may be identified with equivariant cohomology. Via identification Deligne-Mumford is rationally isomorphic to rational coarse moduli space. The theory presented focus on smooth and stable curves.

We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using equivariant and localization in K-theory together with some basic commutative algebra Artin rings.

.Multireference alignment (MRA) is the problem of recovering a signal from its multiple noisy copies, each acted upon by random group element. MRA mainly motivated single-particle cryo–electron microscopy (cryo-EM) that has recently joined X-ray crystallography as one two leading technologies to reconstruct biological molecular structures. Previous papers have shown that, in high-noise regime, sample complexity and cryo-EM \(n=\omega (\sigma^{2d})\), where \(n\) number observations,...