Degree-one displacements on Mars

Degree-1 mantle convection and the crustal dichotomy on Mars

The surface of Mars consists of an old, heavily cratered and elevated southern hemisphere and younger, resurfaced and depressed northern hemisphere, a feature often termed the crustal dichotomy. The global crustal structure [Zuber et al., 2000] revealed by topography and gravity data from the Mars Global Surveyor spacecraft, and the possible late formation of the boundary zone between the hemis...

Jacobi Forms of Degree One

We show that a certain subspace of space of elliptic cusp forms is isomorphic as a Hecke module to a certain subspace of space of Jacobi cusp forms of degree one with matrix index by constructing an explicit lifting. This is a partial generalization of the work of Skoruppa and Zagier. This lifting is also related with the Ikeda lifting.

Flexible Algebras of Degree One

Rational Points on Certain Del Pezzo Surfaces of Degree One

Let f(z) = z +az + bz + cz+ d ∈ Z[z] and let us consider a del Pezzo surface of degree one given by the equation Ef : x 2 − y − f(z) = 0. In this note we prove that if the set of rational points on the curve Ea, b : Y 2 = X + 135(2a − 15)X − 1350(5a + 2b − 26) is infinite, then the set of rational points on the surface Ef is dense in the Zariski topology.

On Borel Fixed Ideals Generated in One Degree

We construct a (shellable) polyhedral cell complex that supports a minimal free resolution of a Borel fixed ideal, which is minimally generated (in the Borel sense) by just one monomial in S = k[x1, x2, ..., xn]; this includes the case of powers of the homogeneous maximal ideal (x1, x2, ..., xn) as a special case. In our most general result we prove that for any Borel fixed ideal I generated in...