Search results for "Hypersurface"
showing 10 items of 48 documents
Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces
2003
Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space, ramified over a hypersurface of degree d. Iterating this construction, one obtains M(d,n;r). We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa coupling degenerates for d<2n. On the other hand, for all d>n the sub-stack M(d,n;2) deforms. We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r), and we construct a 4-dimensional family of quintic hypersurfaces, and a dense set of points in the base, where the fibres ha…
Geometry of the projectivization of ideals and applications to problems of birationality
2018
In this thesis, we interpret geometrically the torsion of the symmetric algebra of the ideal sheaf I_Z of a scheme Z defined by n+1 equations in an n-dimensional variety. This is equivalent to study the geometry of the projectivization of I_Z. The applications of this point of view concern, in particular, the topic of birational maps of the projective space of dimension 3 for which we construct explicit birational maps that have the same algebraic degree as their inverse, free and nearly-free curves for which we generalise a characterization of free curves by extending the notion of Milnor and Tjurina numbers. We tackle also the topic of homaloidal hypersurfaces, our original motivation, fo…
A study of coronene?coronene association using atom?atom pair potentials
1996
A study of the coronene—coronene association using different interaction potentials based on an atom-atom pair potential proposed by Fraga has been performed. The interaction potentials employed differ in the way the electrostatic and/or dispersion contributions are computed. The influence of both contributions on the geometries predicted for the coronene dimer is discussed in order to analyze the effectiveness of the different interaction potentials. The stationary points found in each interaction energy hypersurface are characterized by calculating the Hessian eigenvalues. Results are discussed in the light of those previously reported for the benzene dimer. Stacked-displaced structures a…
The Coble Quadric
2023
Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the Coble quartic. Gruson, Sam and Weyman realized that this quartic could be constructed from a general skew-symmetric fourform in eight variables. Using the lines contained in the quartic, we prove that a similar construction allows to recover SU$_C(2, L)$, the moduli space of rank two stable vector bundles on C with fixed determinant of odd degree L, as a subvariety of $G(2, 8)$. In fact, each point $p \in C$ defines a natural embedding of SU$_C(2, \mathca…
Comparing the relative volume with a revolution manifold as a model
1993
Given a pair (P, M), whereM is ann-dimensional connected compact Riemannian manifold andP is a connected compact hypersurface ofM, the relative volume of (P, M) is the quotient volume(P)/volume(M). In this paper we give a comparison theorem for the relative volume of such a pair, with some bounds on the Ricci curvature ofM and the mean curvature ofP, with respect to that of a model pair\(\left( {\mathcal{P},\mathcal{M}} \right)\) where ℳ is a revolution manifold and\(\mathcal{P}\) a “parallel” of ℳ.
Slow-roll corrections in multi-field inflation: a separate universes approach
2018
In view of cosmological parameters being measured to ever higher precision, theoretical predictions must also be computed to an equally high level of precision. In this work we investigate the impact on such predictions of relaxing some of the simplifying assumptions often used in these computations. In particular, we investigate the importance of slow-roll corrections in the computation of multi-field inflation observables, such as the amplitude of the scalar spectrum $P_\zeta$, its spectral tilt $n_s$, the tensor-to-scalar ratio $r$ and the non-Gaussianity parameter $f_{NL}$. To this end we use the separate universes approach and $\delta N$ formalism, which allows us to consider slow-roll…
Zero rest-mass fields and the Newman-Penrose constants on flat space
2020
Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman-Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, Friedrich's framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance $\rho$ to spatial infinity, the NP constants correspond to the data for the second highest possible spherical harmonic …
ChemInform Abstract: Excitation of Nucleobases from a Computational Perspective I: Reaction Paths
2016
The main intrinsic photochemical events in nucleobases can be described on theoretical grounds within the realm of non-adiabatic computational photochemistry. From a static standpoint, the photochemical reaction path approach (PRPA), through the computation of the respective minimum energy path (MEP), can be regarded as the most suitable strategy in order to explore the electronically excited isolated nucleobases. Unfortunately, the PRPA does not appear widely in the studies reported in the last decade. The main ultrafast decay observed experimentally for the gas-phase excited nucleobases is related to the computed barrierless MEPs from the bright excited state connecting the initial Franck…
An ab initio study of the unimolecular decomposition mechanism of formamidine. 4-31G Characterization of potential energy hypersurface
1991
Ab initio MO calculations have been carried out for the unimolecular decomposition of formamidine. The Hartree–Fock method in LCAO approximation with the 4-31G basis set was used. The 4-31G potential hypersurface has been further studied. The stationary points (R, TS, and P) were localized. A reaction analysis by correlation of bond-order indices and localized molecular orbitals demonstrated that the decomposition is an asynchronous process. The TS can be described as four-membered ring.
Champs de vecteurs analytiques et champs de gradients
2002
A theorem of Łojasiewicz asserts that any relatively compact solution of a real analytic gradient vector field has finite length. We show here a generalization of this result for relatively compact solutions of an analytic vector field X with a smooth invariant hypersurface, transversally hyperbolic for X, where the restriction of the field is a gradient. This solves some instances of R. Thom's Gradient Conjecture. Furthermore, if the dimension of the ambient space is three, these solutions do not oscillate (in the sense that they cut an analytic set only finitely many times); this can also be applied to some gradient vector fields.