arXiv subjects

R. Miranda

Publications and source records attributed to R. Miranda.

24 records · Page 2Linked to original sources

arXiv2004

Non-stochastic behavior of atomic surface diffusion on Cu(111) at all temperatures

Atomic diffusion is usually understood as a succession of random, independent displacements of an adatom over the surface's potential energy landscape. Nevertheless, an analysis of Molecular Dynamics simulations of self-diffusion on Cu(111) demonstrates the existence of different types of correlations in the atomic jumps at all temperatures. Thus, the atomic displacements cannot be correctly described in terms of a random walk model. This fact has a profound impact on the determination and interpretation of diffusion coefficients.

cond-mat.other↗

arXiv2003

On the geometric genus of reducible surfaces and degenerations of surfaces to unions of planes

In this paper we study some properties of degenerations of surfaces whose general fibre is a smooth projective surface and whose central fibre is a reduced, connected surface $X \subset IP^r$, $r \geq 3$, which is assumed to be a union of smooth projective surfaces, in particular of planes. Our original motivation has been a series of papers of G. Zappa which appeared in the 1940-50's regarding degenerations of scrolls to unions of planes. Here, we present a first set of results on the subject; other aspects are still work in progress and will appear later. We first study the geometry and the combinatorics of a surface like $X$, considered as a reduced, connected surface on its own; then we focus on the case in which X is the central fibre of a degeneration of relative dimension two over the complex unit disk. In this case, we deduce some of the intrinsic and extrinsic invariants of the general fibre from the ones of its central fibre. In the particular case of $X$ a central fibre of a semistable degeneration, i.e. $X$ has only global normal crossing singularities and the total space of the degeneration is smooth, some of the above invariants can be also computed by topological methods (i.e., the Clemens-Schmid exact sequence). Our results are more general, not only because the computations are independent on the fact that $X$ is the central fibre of a degeneration, but also because the degeneration is not semistable in general.

math.AG↗

arXiv2000

Detecting Electronic States at Stacking Faults in Magnetic Thin Films by Tunneling Spectroscopy

Co islands grown on Cu(111) with a stacking fault at the interface present a conductance in the empty electronic states larger than the Co islands that follow the stacking sequence of the Cu substrate. Electrons can be more easily injected into these faulted interfaces, providing a way to enhance transmission in future spintronic devices. The electronic states associated to the stacking fault are visualized by tunneling spectroscopy and its origin is identified by band structure calculations.

cond-mat.mtrl-sci↗

arXiv1998

Degenerations of Planar Linear Systems

Fixing $n$ general points $p_i$ in the plane, what is the dimension of the space of plane curves of degree $d$ having multiplicity $m_i$ at $p_i$ for each $i$? In this article we propose an approach to attack this problem, and demonstrate it by successfully computing this dimension for all $n$ and for $m_i$ constant, at most 3. This application, while previously known (see \cite{hirschowitz1}), demonstrates the utility of our approach, which is based on an analysis of the corresponding linear system on a degeneration of the plane itself, leading to a simple recursion for these dimensions. We also obtain results in the ``quasi-homogeneous'' case when all the multiplicities are equal except one; this is the natural family to consider in the recursion.

alg-geom↗

arXiv1998

Linear Systems of Plane Curves with Base Points of Equal Multiplicity

In this article we address the problem of computing the dimension of the space of plane curves of degree $d$ with $n$ general points of multiplicity $m$. A conjecture of Harbourne and Hirschowitz implies that when $d \geq 3m$, the dimension is equal to the expected dimension given by the Riemann-Roch Theorem. Also, systems for which the dimension is larger than expected should have a fixed part containing a multiple $(-1)$-curve. We reformulate this conjecture by explicitly listing those systems which have unexpected dimension. Then we use a degeneration technique developed in a previous article ("Degenerations of Planar Linear Systems", alg-geom/9702015) to show that the conjecture holds for all $m \leq 12$.

math.AG↗

arXiv1994

On the Corank of Gaussian Maps for General Embedded K3 Surfaces

Let $S_{g}$ be a general prime K3 surface in $P^g$ of genus $g \geq 3$ or a general double cover of $P^2$ ramified along a sextic curve for $g = 2$ and $S = S_{i,g}$ its {\it i}-th Veronese embedding. In this article we compute the corank of the Gaussian map $Φ:\bigwedge^2 H^0(S,O_S(1)) \to H^0(S,Ω_S^1(2))$ for $i \geq 2, g \geq 2$ and $i=1, g \geq 17$. The main idea is to reduce the surjectivity of $Φ$ to an application of the Kawamata-Viehweg vanishing theorem on the blow-up of $S \times S$ along,the diagonal. This is seen to apply once the hyperplane divisor of the K3 surface $S$ can be decomposed as a sum of three suitable birationally ample divisors. We show that such a decomposition exists when $i \geq 3$ or on some K3 surfaces, constructed using the surjectivity of the period mapping, when $i = 1, g \geq 17$ or $i=2, g \geq 7$.

alg-geom↗