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In this article we investigate deformations of a scalar-flat Kähler metric on the total space of complex line bundles over CP^1 constructed by C. LeBrun. In particular, we find that the metric is included in a one-dimensional family of such metrics...
In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain to the othe...
Motivated by applications to higher-rank Brill-Noether theory and the Bertram-Feinberg-Mukai conjecture, we introduce the concepts of linked alternating and linked symplectic forms on a chain of vector bundles, and show that the linked symplectic Gra...
measurements 25 sheets = 1 quire 500 sheets = 20 quires = 1 ream 1,000 sheets = 40 quires = 2 reams = 1 bundle 5,000 sheets = 200 quires = 10 reams = 5 bundles
The Mac@IBM enrollment app makes setting up macOS with Jamf Pro more intuitive for users and easier for IT. The application offers IT admins the ability to gather additional information about their users during setup, allows users to customize their enrollment by selecting apps o…
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Here we prove that for a smooth projective variety $X$ of arbitrary dimension and for a vector bundle $E$ over $X$, the Harder-Narasimhan filtration of a Frobenius pull back of $E$ is a refinement of the Frobenius pull-back of the Harder-Narasimhan f...
18 hours ago · AI algorithm enables tracking of vital white matter pathways Opening a new window on the brainstem, a new tool reliably and finely resolves distinct nerve bundles in live diffusion MRI …
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Fix a point $t_0$ in the circle $S^1$. The space $J^k(t_0, \mathbb{P}^1)$ of $k$-jets at $t_0$ of $C^{\infty}$ maps from $S^1$ to the Riemann sphere $\mathbb{P}^1$ is a $k+1$ dimensional complex algebraic manifold. We identify a class of holomorphic...
The loop space $L\mathbb{P}_1$ of the Riemann sphere consisting of all $C^k$ or Sobolev $W^{k,p}$ maps from the circle $S^1$ to $\mathbb{P}_1$ is an infinite dimensional complex manifold. The loop group $LPGL(2,\mathbb{C})$ acts on $L\mathbb{P}_1$ ....
The loop space of the Riemann sphere consisting of all $C^k$ or Sobolev $W^{k,p}$ maps from the circle $S^1$ to the sphere is an infinite dimensional complex manifold. We compute the Picard group of holomorphic line bundles on this loop space as an i...
Several intrinsic topological ways to encode connections on vector bundles on smooth complex algebraic curves will be described. In particular the notion of {\em Stokes decompositions} will be formalised, as a convenient intermediate category between...
This paper proposes a novel school choice system where schools are grouped into hierarchical bundles and offered to students as options for preference reports. By listing a bundle, a student seeks admission to any school within it without ranking the...
We define generalized Atiyah-Patodi-Singer boundary conditions of product type for Dirac operators associated to C*-vector bundles on the product of a compact manifold with boundary and a closed manifold. We prove a product formula for the K-theore...
We define and investigate extension groups in the context of Arakelov geometry. The 'arithmetic extension groups' we introduce are extensions by groups of analytic types of the usual extension groups attached to $Ø_X$-modules over an arithmetic sc...
We present a conjecture in Diophantine geometry concerning the construction of line bundles over smooth projective varieties over $\bar{\mathbb Q}}$. This conjecture, closely related to the Grothendieck Period Conjecture for cycles of codimension 1,...
In this work, we describe how to obtain the structure of an infinite-dimensional Lie group on the group of compactly carried bundle automorphisms Autc(P) for a locally convex prinicpal bundle P over a finite-dimensional smooth sigma-compact base M. T...
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This thesis is concerned with the residues modulo 4 and 8 of the signature of a 4k-dimensional oriented geometric Poincare complex. The Z_8-valued Brown-Kervaire invariant of Z_4-valued quadratic forms is used to prove that if the signature is divisi...
5 days ago · AI algorithm enables tracking of vital white matter pathways Opening a new window on the brainstem, a new tool reliably and finely resolves distinct nerve bundles in live diffusion MRI scans, …
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We discuss the stationary states of a model economy in which $N$ heterogeneous adaptive consumers purchase commodity bundles repeatedly from $P$ sellers. The system undergoes a transition from an inefficient to an efficient state as the number of c...
5 days ago · AI algorithm enables tracking of vital white matter pathways Opening a new window on the brainstem, a new tool reliably and finely resolves distinct nerve bundles in live diffusion MRI scans, …
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In the first part we use Gromov's K--area to define the K--area homology which stabilizes into singular homology on the category of pairs of compact smooth manifolds. The second part treats the questions of certain curvature gaps. For instance, the $...
A double disk bundle is any smooth closed manifold obtained as the union of the total spaces of two disk bundles, glued together along their common boundary. The Double Soul Conjecture asserts that a closed simply connected manifold admitting a metri...
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We construct Mori Dream Spaces as fine moduli spaces of representations of bound quivers, thereby extending results of Craw--Smith \cite{CrawSmith} beyond the toric case. Any collection of effective line bundles $\mathscr{L}=(\mathscr{O}_X, L_1,...,...
Incel discourse bundles together several psychologically powerful themes at once. First, it centers on sex and status—two domains that are evolutionarily consequential and culturally salient. Becaus...
5 days ago · AI algorithm enables tracking of vital white matter pathways Opening a new window on the brainstem, a new tool reliably and finely resolves distinct nerve bundles in live diffusion MRI scans, …
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5 days ago · AI algorithm enables tracking of vital white matter pathways Opening a new window on the brainstem, a new tool reliably and finely resolves distinct nerve bundles in live diffusion MRI scans, …
This article highlights the ToricHigherDirectImages package in Macaulay2. The central feature is a method for computing (higher) direct images of line bundles under surjective toric morphisms....
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Also, if I'm not mistaken, Steenrod gives a more direct argument in "Topology of Fibre Bundles," but he might be using the long exact sequence of a fibration (which you mentioned).
We introduce higher analogs for cleavages in the context of (Kan) simplicial fibrations. We apply them to obtain geometric models for representations up to homotopy of (higher) Lie groupoids. Concretely, we set an equivalence between representations...