scholarly journals Window shifts, flop equivalences and Grassmannian twists

2014 ◽  
Vol 150 (6) ◽  
pp. 942-978 ◽  
Author(s):  
Will Donovan ◽  
Ed Segal
Keyword(s):  
Vector Bundles ◽  
Derived Categories ◽  
Geometric Construction ◽  
Algebraic Construction ◽  
New Class ◽  
Spherical Twists

AbstractWe introduce a new class of autoequivalences that act on the derived categories of certain vector bundles over Grassmannians. These autoequivalences arise from Grassmannian flops: they generalize Seidel–Thomas spherical twists, which can be seen as arising from standard flops. We first give a simple algebraic construction, which is well suited to explicit computations. We then give a geometric construction using spherical functors which we prove is equivalent.

Algebraic construction of a new class of quasi-orthogonal arrays for steganography

1999 ◽  
Author(s):  
Ron G. van Schyndel ◽  
Andrew Z. Tirkel ◽  
Imants D. Svalbe ◽  
Thomas E. Hall ◽  
Charles F. Osborne
Keyword(s):  
Orthogonal Arrays ◽  
Algebraic Construction ◽  
New Class

scholarly journals QUILLEN EQUIVALENT MODELS FOR THE DERIVED CATEGORY OF FLATS AND THE RESOLUTION PROPERTY

2020 ◽  
pp. 1-19
Author(s):  
SERGIO ESTRADA ◽  
ALEXANDER SLÁVIK
Keyword(s):  
Vector Bundles ◽  
Derived Categories ◽  
Derived Category ◽  
Projective Modules ◽  
Dimensional Vector ◽  
Infinite Dimensional ◽  
Equivalent Models ◽  
Flat Modules ◽  
Quillen Equivalent ◽  
Resolution Property

We investigate the assumptions under which a subclass of flat quasicoherent sheaves on a quasicompact and semiseparated scheme allows us to ‘mock’ the homotopy category of projective modules. Our methods are based on module-theoretic properties of the subclass of flat modules involved as well as their behaviour with respect to Zariski localizations. As a consequence we get that, for such schemes, the derived category of flat quasicoherent sheaves is equivalent to the derived category of very flat quasicoherent sheaves. If, in addition, the scheme satisfies the resolution property then both derived categories are equivalent to the derived category of infinite-dimensional vector bundles. The equivalences are inferred from a Quillen equivalence between the corresponding models.

scholarly journals Moduli of vector bundles on higher-dimensional base manifolds — Construction and variation

2016 ◽  
Vol 27 (07) ◽  
pp. 1650054 ◽  
Author(s):  
Daniel Greb ◽  
Julius Ross ◽  
Matei Toma
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Recent Progress ◽  
Geometric Construction ◽  
Quiver Representations ◽  
Natural Morphism ◽  
Moduli Spaces Of Sheaves ◽  
Higher Dimensional ◽  
Moduli Of Vector Bundles

We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson–Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker–Maruyama moduli spaces with respect to two different chosen polarizations are related via Thaddeus-flips through other “multi-Gieseker”-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding Donaldson–Uhlenbeck moduli space.

scholarly journals Toric vector bundles: GAGA and Hodge theory

2020 ◽  
Author(s):  
Jonas Stelzig
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Hodge Theory ◽  
Algebraic Construction ◽  
Smooth Base

Abstract We prove a GAGA-style result for toric vector bundles with smooth base and give an algebraic construction of the Frölicher approximating vector bundle that has recently been introduced by Dan Popovici using analytic techniques. Both results make use of the Rees-bundle construction.

Torsion Elements and the Classification of Vector Bundles

1977 ◽  
Vol 29 (2) ◽  
pp. 327-332
Author(s):  
Robert D. Little
Keyword(s):  
Algebraic Topology ◽  
Cohomology Class ◽  
Cohomology Group ◽  
Vector Bundles ◽  
Geometric Construction ◽  
Integral Cohomology

There are many situations in algebraic topology when a geometric construction is possible if, and only if, a certain integral cohomology class, an obstruction is zero. When attempts are made to compute the obstruction, it often happens that it is relatively easy to show that m times the obstruction is zero, where m is an integer, and consequently the geometric construction is possible if the cohomology group in question has no elements of order m.

In Situ microscopy of the anodic etching of silicon

1995 ◽  
Vol 53 ◽  
pp. 232-233
Author(s):  
Frances M. Ross ◽  
Peter C. Searson
Keyword(s):  
Composite Structures ◽  
High Surface ◽  
High Surface Area ◽  
Chemical Properties ◽  
Selective Etching ◽  
Silicon On Insulator ◽  
Second Phase ◽  
Porous Layers ◽  
New Class ◽  
Porous Semiconductors

Porous semiconductors represent a relatively new class of materials formed by the selective etching of a single or polycrystalline substrate. Although porous silicon has received considerable attention due to its novel optical properties1, porous layers can be formed in other semiconductors such as GaAs and GaP. These materials are characterised by very high surface area and by electrical, optical and chemical properties that may differ considerably from bulk. The properties depend on the pore morphology, which can be controlled by adjusting the processing conditions and the dopant concentration. A number of novel structures can be fabricated using selective etching. For example, self-supporting membranes can be made by growing pores through a wafer, films with modulated pore structure can be fabricated by varying the applied potential during growth, composite structures can be prepared by depositing a second phase into the pores and silicon-on-insulator structures can be formed by oxidising a buried porous layer. In all these applications the ability to grow nanostructures controllably is critical.

The microtubule associated protein (MAP) tau forms a new class of triple-stranded left-hand helical fibrous protein polymer

1992 ◽  
Vol 50 (1) ◽  
pp. 540-541
Author(s):  
G. C. Ruben ◽  
K. Iqbal ◽  
I. Grundke-Iqbal ◽  
H. Wisniewski ◽  
T. L. Ciardelli ◽  
...  
Keyword(s):  
Axial Ratio ◽  
Normal Structure ◽  
Paired Helical Filaments ◽  
Left Hand ◽  
New Class ◽  
Protein Polymer ◽  
Fibrous Protein ◽  
Protein Map ◽  
Neurotransmitter Transport ◽  
Alzheimer Neurofibrillary Tangles

In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.

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