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Journal articles on the topic 'Hilbert strata'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Yu, Chia-Fu, Ching-Li Chai, and Frans Oort. "Stratifying Lie Strata of Hilbert Modular Varieties." Taiwanese Journal of Mathematics 24, no. 6 (December 2020): 1307–52. http://dx.doi.org/10.11650/tjm/200305.

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2

Fumasoli, Stefan. "Hilbert scheme strata defined by bounding cohomology." Journal of Algebra 315, no. 2 (September 2007): 566–87. http://dx.doi.org/10.1016/j.jalgebra.2007.04.016.

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3

Erman, Daniel. "Murphy’s law for Hilbert function strata in the Hilbert scheme of points." Mathematical Research Letters 19, no. 6 (2012): 1277–81. http://dx.doi.org/10.4310/mrl.2012.v19.n6.a8.

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4

Lederer, Mathias. "Gröbner strata in the Hilbert scheme of points." Journal of Commutative Algebra 3, no. 3 (September 2011): 349–404. http://dx.doi.org/10.1216/jca-2011-3-3-349.

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5

Mall, Daniel. "Connectedness of Hilbert function strata and other connectedness results." Journal of Pure and Applied Algebra 150, no. 2 (June 2000): 175–205. http://dx.doi.org/10.1016/s0022-4049(99)00068-7.

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6

Göttsche, Lothar. "Betti numbers for the hilbert function strata of the punctual hilbert scheme in two variables." Manuscripta Mathematica 66, no. 1 (December 1990): 253–59. http://dx.doi.org/10.1007/bf02568495.

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7

Ran, Ziv. "Incidence stratifications on Hilbert schemes of smooth surfaces, and an application to Poisson structures." International Journal of Mathematics 27, no. 01 (January 2016): 1650006. http://dx.doi.org/10.1142/s0129167x16500063.

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Given a smooth curve on a smooth surface, the Hilbert scheme of points on the surface is stratified according to the length of the intersection with the curve. The strata are highly singular. We show that this stratification admits a natural log-resolution, namely the stratified blowup. As a consequence, the induced Poisson structure on the Hilbert scheme of a Poisson surface has unobstructed deformations.

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8

Lederer, Mathias. "Components of Gröbner strata in the Hilbert scheme of points." Proceedings of the London Mathematical Society 108, no. 1 (July 12, 2013): 187–224. http://dx.doi.org/10.1112/plms/pdt018.

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9

Shende, Vivek. "Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation." Compositio Mathematica 148, no. 2 (January 26, 2012): 531–47. http://dx.doi.org/10.1112/s0010437x11007378.

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AbstractLet C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central point are determined by the Euler numbers of the Hilbert schemes of points on C. These Euler numbers have made two prior appearances. First, in certain simple cases, they control the contribution of C to the Pandharipande–Thomas curve counting invariants of three-folds. In this context, our result identifies the strata multiplicities as the local contributions to the Gopakumar–Vafa BPS invariants. Second, when C is smooth away from a unique singular point, a conjecture of Oblomkov and the present author identifies the Euler numbers of the Hilbert schemes with the ‘U(∞)’ invariant of the link of the singularity. We make contact with combinatorial ideas of Jaeger, and suggest an approach to the conjecture.

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10

Dong, Lihu, Danqing Song, and Guangwei Liu. "Seismic Wave Propagation Characteristics and Their Effects on the Dynamic Response of Layered Rock Sites." Applied Sciences 12, no. 2 (January 12, 2022): 758. http://dx.doi.org/10.3390/app12020758.

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To investigate the seismic response of layered rock sites, a multidomain analysis method was proposed. Three finite element models with infinite element boundaries for layered sites were analysed. The results of this multidomain analysis show that stratum properties and elevation have an impact on wave propagation characteristics and the dynamic response of layered sites. Compared with the rock mass, the overlying gravel soil has a greater dynamic amplification effect at the sites. A time domain analysis parameter PGA(IMF) was proposed to analyse the effects of different strata on the seismic magnification effect of layered sites, and its application was also discussed in comparison with PGA. According to the frequency domain analysis, the interface of the rock mass strata has a low impact on the Fourier spectrum characteristics of the sites, but gravel soil has a great magnification effect on the spectrum amplitude in the high-frequency band (≥30 Hz) of waves. Moreover, the stratum properties have a great influence on the shape and peak value of the Hilbert energy and marginal spectrum at layered sites. When waves propagate from hard rock to soft rock, the peak value of the Hilbert energy spectrum changes from single to multiple peaks; then, in gravelly soil, the Hilbert energy spectral peak, its nearby amplitude and the amplitude in the high-frequency band (28–36 Hz) are obviously amplified. The frequency components and amplitude of the marginal spectrum become more abundant and larger from rock to gravelly soil in the high-frequency band (28–35 Hz).

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11

LEMMA, FRANCESCO. "ON THE RESIDUE OF EISENSTEIN CLASSES OF SIEGEL VARIETIES." Glasgow Mathematical Journal 60, no. 3 (October 30, 2017): 539–53. http://dx.doi.org/10.1017/s0017089517000271.

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AbstractEisenstein classes of Siegel varieties are motivic cohomology classes defined as pull-backs by torsion sections of the polylogarithm prosheaf on the universal abelian scheme. By reduction to the Hilbert–Blumenthal case, we prove that the Betti realization of these classes on Siegel varieties of arbitrary genus have non-trivial residue on zero-dimensional strata of the Baily–Borel–Satake compactification. A direct corollary is the non-vanishing of a higher regulator map.

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12

De Naeghel, Koen, and Michel Van den Bergh. "On incidence between strata of the Hilbert scheme of points on $$\mathbb{P}^{2}$$." Mathematische Zeitschrift 255, no. 4 (November 15, 2006): 897–922. http://dx.doi.org/10.1007/s00209-006-0057-4.

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13

Fuchs, E., P. D. Jarvis, G. Rudolph, and M. Schmidt. "The Hilbert space costratification for the orbit type strata of SU(2)-lattice gauge theory." Journal of Mathematical Physics 59, no. 8 (August 2018): 083505. http://dx.doi.org/10.1063/1.5031115.

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14

Kleppe, Jan O. "The Smoothness and the Dimension ofPGor(H) and of Other Strata of the Punctual Hilbert Scheme." Journal of Algebra 200, no. 2 (February 1998): 606–28. http://dx.doi.org/10.1006/jabr.1997.7226.

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15

Yan, Binpeng, Sanyi Yuan, Shangxu Wang, Yonglin OuYang, Tieyi Wang, and Peidong Shi. "Improved eigenvalue-based coherence algorithm with dip scanning." GEOPHYSICS 82, no. 2 (March 1, 2017): V95—V103. http://dx.doi.org/10.1190/geo2016-0149.1.

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Detection and identification of subsurface anomalous structures are key objectives in seismic exploration. The coherence technique has been successfully used to identify geologic abnormalities and discontinuities, such as faults and unconformities. Based on the classic third eigenvalue-based coherence ([Formula: see text]) algorithm, we make several improvements and develop a new method to construct covariance matrix using the original and Hilbert transformed seismic traces. This new covariance matrix more readily converges to the main effective signal energy on the largest eigenvalue by decreasing all other eigenvalues. Compared with the conventional coherence algorithms, our algorithm has higher resolution and better noise immunity ability. Next, we incorporate this new eigenvalue-based algorithm with time-lag dip scanning to relieve the dip effect and highlight the discontinuities. Application on 2D synthetic data demonstrates that our coherence algorithm favorably alleviates the low-valued artifacts caused by linear and curved dipping strata and clearly reveals the discontinuities. The coherence results of 3D real field data also commendably suppress noise, eliminate the influence of large dipping strata, and highlight small hidden faults. With the advantages of higher resolution and robustness to random noise, our strategy successfully achieves the goal of detecting the distribution of discontinuities.

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16

EICHHORN, JÜRGEN. "GAUGE THEORY ON OPEN MANIFOLDS OF BOUNDED GEOMETRY." International Journal of Modern Physics A 07, no. 17 (July 10, 1992): 3927–77. http://dx.doi.org/10.1142/s0217751x92001769.

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On compact manifolds (Mn, g) and for r>n/2+1 the configuration space [Formula: see text] is a well-defined object. [Formula: see text] is an affine space with a Sobolev space as vector space, and [Formula: see text] a Hilbert Lie group which acts smoothly and properly on [Formula: see text]. [Formula: see text] is a stratified space with Hilbert manifolds as strata. The existence problem has been solved for many interesting cases by Cliff Taubes and the description of the moduli space of instantons has been given by Donaldson. On noncompact manifolds none of the approaches of the compact case is further valid. We present here an intrinsic, self-consistent approach for gauge theory on open manifolds of bounded geometry up to order n/2+2. The main idea is to endow the space CP of gauge potentials and the gauge group with an intrinsic Sobolev topology. Bounded geometry of the underlying manifold and the considered connections provides all the Sobolev theorems which are needed to prove the existence of instantons if G=SU(2). We prove the existence of instantons if (M4, g) satisfies a certain spectral condition and has a positive definite L2 intersection form.

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17

Feng, Z. "The seismic signatures of the 2009 Shiaolin landslide in Taiwan." Natural Hazards and Earth System Sciences 11, no. 5 (May 25, 2011): 1559–69. http://dx.doi.org/10.5194/nhess-11-1559-2011.

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Abstract. The Shiaolin landslide occurred on 9 August 2009 after Typhoon Morakot struck Taiwan, claiming over 400 lives. The seismic signals produced by the landslide were recorded by broadband seismic stations in Taiwan. The time-frequency spectra for these signals were obtained by the Hilbert-Huang transform (HHT) and were analyzed to obtain the seismic characteristics of the landslide. Empirical mode decomposition (EMD) was applied to differentiate weak surface-wave signals from noise and to estimate the surface-wave velocities in the region. The surface-wave velocities were estimated using the fifth intrinsic mode function (IMF 5) obtained from the EMD. The spectra of the earthquake data were compared. The main frequency content of the seismic waves caused by the Shiaolin landslide were in the range of 0.5 to 1.5 Hz. This frequency range is smaller than the frequency ranges of other earthquakes. The spectral analysis of surface waves (SASW) method is suggested for characterizing the shear-wave velocities of the strata in the region.

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18

Guo, Xuebao, Ying Shi, Weihong Wang, Hongliang Jing, and Zhen Zhang. "Wavefield decomposition in arbitrary direction and an imaging condition based on stratigraphic dip." GEOPHYSICS 85, no. 5 (August 17, 2020): S299—S312. http://dx.doi.org/10.1190/geo2019-0617.1.

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In reverse time migration (RTM), wavefield decomposition can play an important role in addressing the issue of migration noise, especially low-frequency noise. The complete wavefield decomposition based on the Hilbert transform is a commonly used method in RTM, but it is accompanied by extra wavefield simulation and wavefield storage. We have developed three distinct methods. The first is a convenient method for wavefield decomposition, which is based on Poynting vectors. Only the unit vector in one direction is needed to realize the wavefield decomposition in an arbitrary direction by this method. It breaks through the limitation that the Hilbert transform-based method is applicable only to the up- and downgoing wave or left- and right-going wave decomposition, and the calculation cost is negligible compared with RTM. The second is a method based on the instantaneous wavenumber, which we developed for calculating the wave propagation direction. On the basis of wavefield decomposition, the imaging angle gather from the new method performs better than that of the Poynting vector method. Meanwhile, it also is used for generating the incident angle gather and dip angle gather. The latter expresses the dip angle of underground strata. More importantly, the above methods allow us to control the wavefield decomposition direction and three angles at any position underground. The third adopts a stratigraphic imaging condition method, and we briefly analyze the relationship between the new method and the inverse-scattering imaging condition. The stratigraphic imaging condition maps the results to the dip angle of the stratum through a spatial gradient wavefield, which can enhance the effective imaging information. The above three kinds of angle gathers also can be constructed by the stratigraphic imaging condition. Numerical experiments demonstrate that the imaging results and the angle gathers obtained by our proposed method have higher accuracy and resolution.

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19

Chen, Lijun, Jianxun Chen, Yanbin Luo, Yalong Guo, Yongjun Mu, Daochuan Zhong, Weiwei Liu, Tielun Yang, and Weixiang Chen. "Propagation Laws of Blasting Seismic Waves in Weak Rock Mass: A Case Study of Muzhailing Tunnel." Advances in Civil Engineering 2020 (May 25, 2020): 1–15. http://dx.doi.org/10.1155/2020/8818442.

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In order to study the propagation laws of blasting vibration waves in weak rock tunnels, the longitudinal and circumferential blasting vibration tests in Muzhailing Tunnel were carried out, and the measured data were analyzed and studied using the methods of Sadov’s nonlinear regression, Fourier transform, and Hilbert–Huang transform (HHT) to provide a reference for the optimization of blasting design of Muzhailing Tunnel or similar weak rock tunnels. The results showed that the tangential main frequency decreases rapidly and the radial main frequency decreases slowly with the increase of proportionate charge quantity. Under a certain charge quantity, as the distance from the explosion source increases, the spectrum width of the blasting vibration frequency becomes narrower, the overall energy is more concentrated, and the vibration frequency tends to be closer to the low frequency. At a certain distance from the explosive source, the frequency of blasting vibration decreases gradually, and the amplitude of low-frequency region increases with the increase of charge quantity. The vibration velocity on the left side of the tunnel is larger than that on the right side, and the vibration velocity at the vault and the arch foot of lower bench decreases rapidly, while the vibration velocity at the arch feet of upper bench and middle bench decreases slowly. The vibration frequencies of the left arch foot of the middle bench and the right arch foot of the upper bench are higher than those of other positions, while the frequencies of the left arch foot of the upper bench are the lowest. During tunnel blasting, the energy input to the strata media is mainly concentrated in the stage of the blasting of the cut hole. The blasting has more energy input to the left arch foot of the upper bench and the tunnel vault, which is consistent with the conclusion of frequency analysis.

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20

Zhang, Mengyuan. "Bundles on with vanishing lower cohomologies." Canadian Journal of Mathematics, April 24, 2020, 1–20. http://dx.doi.org/10.4153/s0008414x20000292.

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Abstract We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli $\mathcal{M}$ according to the Hilbert function H and classify all possible Hilbert functions H of such bundles. For each H, we describe a stratification of $\mathcal{M}_H$ by quotients of rational varieties. We show that the closed strata form a graded lattice given by the Betti numbers.

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21

Evain, Laurent, and Mathias Lederer. "Bialynicki-Birula schemes in higher dimensional Hilbert schemes of points and monic functors." Épijournal de Géométrie Algébrique Volume 5 (April 29, 2021). http://dx.doi.org/10.46298/epiga.2021.volume5.5618.

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The Bialynicki-Birula strata on the Hilbert scheme $H^n(\mathbb{A}^d)$ are smooth in dimension $d=2$. We prove that there is a schematic structure in higher dimensions, the Bialynicki-Birula scheme, which is natural in the sense that it represents a functor. Let $\rho_i:H^n(\mathbb{A}^d)\rightarrow {\rm Sym}^n(\mathbb{A}^1)$ be the Hilbert-Chow morphism of the ${i}^{th}$ coordinate. We prove that a Bialynicki-Birula scheme associated with an action of a torus $T$ is schematically included in the fiber $\rho_i^{-1}(0)$ if the ${i}^{th}$ weight of $T$ is non-positive. We prove that the monic functors parametrizing families of ideals with a prescribed initial ideal are representable. Comment: Final version

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