2,501 research outputs found
Quantum intersection rings
We examine a few problems of enumerative geometry and present their solutions
in the framework of deformed (quantum) cohomology rings.Comment: 73 p, uuencoded, uses harvmac in b mode, 6 figures include
Higher dimensional black holes with a generalized gravitational action
We consider the most general higher order corrections to the pure gravity
action in dimensions constructed from the basis of the curvature monomial
invariants of order 4 and 6, and degree 2 and 3, respectively. Perturbatively
solving the resulting sixth-order equations we analyze the influence of the
corrections upon a static and spherically symmetric back hole. Treating the
total mass of the system as the boundary condition we calculate location of the
event horizon, modifications to its temperature and the entropy. The entropy is
calculated by integrating the local geometric term constructed from the
derivative of the Lagrangian with respect to the Riemann tensor over a
spacelike section of the event horizon. It is demonstrated that identical
result can be obtained by integration of the first law of the black hole
thermodynamics with a suitable choice of the integration constant. We show that
reducing coefficients to the Lovelock combination, the approximate expression
describing entropy becomes exact. Finally, we briefly discuss the problem of
field redefinition and analyze consequences of a different choice of the
boundary conditions in which the integration constant is related to the exact
location of the event horizon and thus to the horizon defined mass
Novel insights into the multiplier rule
We present the Lagrange multiplier rule, one of the basic optimization methods, in a new way. Novel features include:• Explanation of the true source of the power of the rule: reversal of tasks, but not the use of multipliers.• A natural proof based on a simple picture, but not the usual technical derivation from the implicit function theorem.• A practical method to avoid the cumbersome second order conditions.• Applications from various areas of mathematics, physics, economics.• Some hnts on the use of the rule.bargaining;dynamical systems;economics;finance;multiplier rule;second order condition
The second moment of twisted modular L-functions
We prove an asymptotic formula with a power saving error term for the (pure
or mixed) second moment of central values of L-functions of any two (possibly
equal) fixed cusp forms f, g twisted by all primitive characters modulo q,
valid for all sufficiently factorable q including 99.9% of all admissible
moduli. The two key ingredients are a careful spectral analysis of a
potentially highly unbalanced shifted convolution problem in Hecke eigenvalues
and power-saving bounds for sums of products of Kloosterman sums where the
length of the sum is below the square-root threshold of the modulus.
Applications are given to simultaneous non-vanishing and lower bounds on higher
moments of twisted L-functions.Comment: 64 page
The rigid limit in Special Kahler geometry; From K3-fibrations to Special Riemann surfaces: a detailed case study
The limiting procedure of special Kahler manifolds to their rigid limit is
studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of
certain singularities. In two examples we consider all the periods in and
around the rigid limit, identifying the nontrivial ones in the limit as periods
of a meromorphic form on the relevant Riemann surfaces. We show how the Kahler
potential of the special Kahler manifold reduces to that of a rigid special
Kahler manifold. We extensively make use of the structure of these Calabi-Yau
manifolds as K3 fibrations, which is useful to obtain the periods even before
the K3 degenerates to an ALE manifold in the limit. We study various methods to
calculate the periods and their properties. The development of these methods is
an important step to obtain exact results from supergravity on Calabi-Yau
manifolds.Comment: 79 pages, 8 figures. LaTeX; typos corrected, version to appear in
Classical and Quantum Gravit
New method for measuring azimuthal distributions in nucleus-nucleus collisions
The methods currently used to measure azimuthal distributions of particles in
heavy ion collisions assume that all azimuthal correlations between particles
result from their correlation with the reaction plane. However, other
correlations exist, and it is safe to neglect them only if azimuthal
anisotropies are much larger than 1/sqrt(N), with N the total number of
particles emitted in the collision. This condition is not satisfied at
ultrarelativistic energies. We propose a new method, based on a cumulant
expansion of multiparticle azimuthal correlations, which allows to measure much
smaller values of azimuthal anisotropies, down to 1/N. It is simple to
implement and can be used to measure both integrated and differential flow.
Furthermore, this method automatically eliminates the major systematic errors,
which are due to azimuthal asymmetries in the detector acceptance.Comment: final version (misprints corrected), to be published in Phys.Rev.
- …