Geometry of the Quartic

Quartic Gauge Couplings fromK3 Geometry

We show how certain F 4 couplings in eight dimensions can be computed using the mirror map and K3 data. They perfectly match with the corresponding heterotic one-loop couplings, and therefore this amounts to a successful test of the conjectured duality between the heterotic string on T 2 and F -theory on K3. The underlying quantum geometry appears to be a 5-fold, consisting of a hyperkähler 4-f...

Tzitzeica geometry of soliton solutions for quartic interaction PDE

Geometric properties of graphs of solutions for the quartic interaction PDE are studied in the present work. Two classes of solutions are considered. One class is represented by soliton solutions, whereas the other class consists of solutions of a first order PDE system, which generates the quartic interaction PDE, in the sense of least squares type action. We prove that for both classes the gr...

On the Stability of the Orthogonally Quartic Functional Equation

Birational Geometry of Quartic 3-folds Ii: the Importance of Being Q-factorial

The paper explores the birational geometry of terminal quartic 3-folds. In doing this I develop a new approach to study maximal singularities with positive dimensional centers. This allows to determine the pliability of a Q-factorial quartic with ordinary double points, and it shows the importance of Q-factoriality in the context of birational geometry of uniruled 3-folds.

A QUARTIC POTENTIAL FOR THE NUCLEONIC QUARKS

We assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the Dirac matrices. Then by making use of a suitable ansatz, the Dirac equation has a very simple solution which is exact. We then have calculated the static properties of the nucleon in the ...