In this chapter, we give the definition of Mordell–Weil lattice (in Sect. 6.5). First, we bring
together the concepts from Chaps. 4 and 5 in order to gain a better understanding of the …

We show that the n-fold integrals χ (n) of the magnetic susceptibility of the Ising model, as
well as various other n-fold integrals of the'Ising class', or n-fold integrals from enumerative …

Let S be a smooth cubic surface over a finite field q)= 1+ aq+ q2 for some a∈{− 2,− 1, 0, 1, 2,
3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special …

We show that the n-fold integrals $\chi^{(n)} $ of the magnetic susceptibility of the Ising
model, as well as various other n-fold integrals of the" Ising class", or n-fold integrals from …

We survey rational points on higher-dimensional algebraic varieties, addressing questions
about existence, density, and distribution with respect to heights. Key examples for existence …

Using the principle that characteristic polynomials of matrices obtained from elements of a
reductive group G over Q typically have splitting field with Galois group isomorphic to the …

In this paper, we consider the following problem: Does there exist a cubic surface over which
contains no line over, yet contains a line over every completion of? This question may be …

In this paper, we study the discriminant of a hypersurface in a weighted projective space with
isolated singularities. We define the discriminant of a hypersurface in ℙ (q 0, q 1, 1,…, 1) …

Fix a prime number ℓ> 2 and let V be a four-dimensional F ℓ-vector space. We classify
subgroups G of Sp (V) with the property that every g∈ G stabilizes a one-dimensional …

Del Pezzo surfaces are surfaces that can be classified by their degree, which is an integer
between 1 and 9. They are named after Pasquale del Pezzo, who studied surfaces of …