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Now showing items 11-20 of 35

#### On the unirationality of del Pezzo surfaces of degree two

(London Mathematical Society, 2014)

Among geometrically rational surfaces, del Pezzo surfaces of degree 2 over a field k containing at least one point are arguably the simplest that are not known to be unirational over k. Looking for k-rational curves on ...

#### Higher-dimensional analogs of Chatelet surfaces

(London Mathematical Society, 2012)

We discuss the geometry and arithmetic of higher-dimensional analogs of Chatelet surfaces; namely, we describe the structure of their Brauer and Picard groups and show that they can violate the Hasse principle. In addition, ...

#### Level structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture

(Elsevier, 2018)

Assuming Lang's conjecture, we prove that for a prime p, number field K, and positive integer g, there is an integer r such that no principally polarized abelian variety A/K has full level-pr structure. To this end, we use ...

#### Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals

(Springer, 2016)

This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. ...

#### Opening gaps in the spectrum of strictly ergodic Schrodinger operators

(European Mathematical Society, 2012)

We consider Schrodinger operators with dynamically defined potentials arising from
continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem
states that the possible gaps in the spectrum ...

#### The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian

(Springer, 2012)

We consider the density of states measure of the Fibonacci Hamiltonian
and show that, for small values of the coupling constant V , this measure
is exact-dimensional and the almost everywhere value dV of the local ...

#### Handle Addition for Doubly-Periodic Scherk Surfaces

(De Gruyter, 2012)

We prove the existence of a family of embedded doubly periodic minimal
surfaces of (quotient) genus g with orthogonal ends that generalizes the classical doubly
periodic surface of Scherk and the genus-one Scherk surface ...

#### Log minimal model program for the moduli space of stable curves: the first flip

(Department of Mathematics, Princeton University, 2013)

We give a geometric invariant theory (GIT) construction of the log canonical model M¯g(α) of the pairs (M¯g,αδ) for α∈(7/10–ϵ,7/10] for small ϵ∈Q+. We show that M¯g(7/10) is isomorphic to the GIT quotient of the Chow variety ...

#### A Birman exact sequence for Aut(Fn)

(Elsevier, 2012)

The Birman exact sequence describes the effect on the mapping class group of a
surface with boundary of gluing discs to the boundary components. We construct an
analogous exact sequence for the automorphism group of a free ...

#### The Weil-Peterson Hessian of Length on Teichmuller Space

(International Press, 2012)

We present a brief but nearly self-contained proof of a formula
for the Weil-Petersson Hessian of the geodesic length of a closed
curve (either simple or not simple) on a hyperbolic surface. The
formula is the sum of the ...