In general, Picard-Fuchs systems in N = 2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independe...

In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.

We describe all of the smooth complete toric threefolds of Picard number 5 with no nontrivial nef line bundles, and show that no such examples exist with Picard number less than 5.

The Pleistocene vertebrate assemblage of Aldabra Atoll has been comparatively well studied. Three Upper Pleistocene fossil localities have been described yielding birds, reptiles and terrestrial molluscs. Those of Bassin Cabri and Bassin Lebine on Ile Picard are undated but must be in excess of 136,000 YBP, whereas Point Hodoul on Malabar Island is circa 100,000 YBP. Aldabra was seemingly compl...

Linear ordinary differential equations (ODEs) with periodic coefficients appear in various interesting applications, such as determining the linear stability regions of systems of vertically driven multiple pendula. Sinha and Butcher [1, 2] have obtained very good approximations to the solutions of such equations by calculating approximate Picard iterates symbolically in the parameters on which...

Motivated by an application to LDPC (low density parity check) algebraic geometry codes described by Voloch and Zarzar, we describe a computational procedure for establishing an upper bound on the arithmetic or geometric Picard number of a smooth projective surface over a finite field, by computing the Frobenius action on p-adic cohomology to a small degree of p-adic accuracy. We have implement...

In this paper we construct the first known explicit family of K3 surfaces defined over the rationals that are proved to have geometric Picard number 3. This family is dense in one of the components of the moduli space of all polarized K3 surfaces with Picard number at least 3. We also use an example from this family to fill a gap in an earlier paper by the first author. In that paper, an argume...

Here we study the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular operators. We treat both the unitary and non-unitary cases of the operators above. We establish quantitatively the pointwise and uniform convergences of these operators to the unit operator by involving the uniform higher modulus of smoothness of a uni...

The Picard scheme of a smooth curve and a smooth complex variety is reduced. In this note we discuss which classes of surfaces in terms of the Enriques–Kodaira classification can have non-reduced Picard schemes and whether there are restrictions on the characteristic of the ground field. It turns out that non-reduced Picard schemes are uncommon in Kodaira dimension κ ≤ 0, that this phenomenon c...

We test R. van Luijk’s method for computing the Picard group of a K3 surface. The examples considered are the resolutions of Kummer quartics in P. Using the theory of abelian varieties, in this case the Picard group may be computed directly. Our experiments show that the upper bounds provided by R. van Luijk’s method are sharp when sufficiently large primes are used. In fact, there are many pri...