Search results for "Mathematics::Algebraic Geometry"
showing 10 items of 167 documents
On the K-stability of complete intersections in polarized manifolds
2011
We consider the problem of existence of constant scalar curvature Kaehler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai-Umemura-Tian like example of Fano 5-fold admitting no Kaehler-Einstein metric and a strong evidence of K-stability of complete intersections on Grassmannians.
Effect of the loading rate on ultimate strength of composites. Application: Pressure vessel slow burst test
2013
International audience; The strength of unidirectional elastic fibre composites is shown to depend on the loading rate as the viscoelastic nature of the matrix results in a fall in breaking load as the rate is reduced. The simulation of the accumulation of fibre breaks leading to failure, takes into account all physical phenomena involved fibre failure, including the stochastic nature of fibre strength, stress transfer through the matrix between reinforcements, interfacial debonding and the viscoelastic nature of the matrix. The kinetics of composite failure are seen to involve the initial formation of random fibre breaks which at higher loads coalesce into clusters of broken fibres. The ra…
Glass fibre strength distribution determined by common experimental methods
2002
The tensile strength of brittle fibres is routinely described by the Weibull distribution. The parameters of the distribution can be obtained from tests on single fibres and fibre bundles or from model composite tests. However, there is growing evidence that the distribution parameters obtained by different experimental techniques differ systematically. In order to investigate the possible causes of such discrepancies, single-fibre tension, fibre bundle, and single-fibre fragmentation tests are employed in this study to obtain strength distribution of commercial E-glass fibres. The results reveal parameter dependence on the approach used to extract the distribution parameters from experimen…
Strong enhancement of the Breit-Wigner-Fano Raman line in carbon nanotube bundles caused by plasmon band formation
2002
We investigate the origin of the Breit-Wigner-Fano line in the Raman spectra of individual single-walled carbon nanotubes and their bundles. Using confocal Raman microscopy and atomic-force microscopy we found that the Breit-Wigner-Fano line intensity increases strongly with the bundle thickness. We confirmed this result by Raman investigations of partially decomposed bundles, which were additionally investigated by transmission electron microscopy. Our random-phase approximation based theory, which identifies the Breit-Wigner-Fano line as an excited band of plasmon-phonon modes, is fully consistent with the experimental results.
Symmetric locally free resolutions and rationality problems
2022
We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over $\mathbb{P}^2$ with discriminant curves of fixed degree. In particular, we construct explicit models of these bundles for some discriminant data. Among others, we obtain various birational models of a nodal Gushel-Mukai fourfold, as well as of a cubic fourfold containing a plane. Finally, we prove stable irrationality of several types of quadric surface bundles.
New examples of Calabi-Yau threefolds and genus zero surfaces
2012
We classify the subgroups of the automorphism group of the product of 4 projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is non-trivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K^2=3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.
Blown-up toric surfaces with non-polyhedral effective cone
2020
We construct examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudo-effective cone, both in characteristic $0$ and in every prime characteristic $p$. As a consequence, we prove that the pseudo-effective cone of the Grothendieck-Knudsen moduli space $\overline M_{0,n}$ of stable rational curves is not polyhedral for $n\geq 10$ in characteristic $0$ and in characteristic $p$, for all primes $p$. Many of these toric surfaces are related to a very interesting class of arithmetic threefolds that we call arithmetic elliptic pairs of infinite order. Their analysis in characteristic $p$ relies on tools of arithmetic geometry and Galois representations in …
Toric G-solid Fano threefolds
2020
We study toric G-solid Fano threefolds that have at most terminal singularities, where G is an algebraic subgroup of the normalizer of a maximal torus in their automorphism groups.
On a question of Mehta and Pauly
2013
In this short note we provide explicit examples in characteristic $p$ on certain smooth projective curves where for a given semistable vector bundle $\mathcal{E}$ the length of the Harder-Narasimhan filtration of $F^\ast \mathcal{E}$ is longer than $p$. This answers a question of Mehta and Pauly raised in arXiv:math/0607565.
Diffeomorphism classes of Calabi-Yau varieties
2016
In this article we investigate diffeomorphism classes of Calabi-Yau threefolds. In particular, we focus on those embedded in toric Fano manifolds. Along the way, we give various examples and conclude with a curious remark regarding mirror symmetry.