Assume that f : X → Y is a surjective generically finite morphism between smooth projective varieties of general type. In general, it is difficult to conclude any birational property of f from the plurigenera ofX and Y . However, Hacon and Pardini in [HP] (Theorem 3) proved the following theorem for varieties of maximal Albanese dimension (i.e. whose Albanese map are generically finite onto the...

A new family of Fq2-maximal curves is presented and some of their properties are investigated.

Abstract. Consider the critical measure-valued processX(t, ·) onRd corresponding to the evolution equation ut = ρ(x)1u−u2.We prove that the maximal order of ρ(x) for having the compact support property for X is different for d = 1 and d ≥ 2: it is O(x3) in one dimension and O(x2) in higher dimensions. These growth orders also turn out to be the maximal orders for the nonexistence of a nonnegati...

Given a1, a2, . . . , an ∈ Z , we examine the set, G, of all nonnegative integer combinations of these ai. In particular, we examine the generating function f(z) = ∑ b∈G z . We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in Z. In ...

We consider the maximal size of families of k-element subsets of an n element set [n] = {1, 2, . . . , n} that satisfy the properties that every r subsets of the family have non-empty intersection, and no ` subsets contain [n] in their union. We show that for large enough n, the largest such family is the trivial one of all ( n−2 k−1 ) subsets that contain a given element and do not contain ano...

Let G = Cn1 ⊕ . . .⊕Cnr with 1 < n1 | . . . |nr be a finite abelian group, d∗(G) = n1 + . . .+ nr−r, and let d(G) denote the maximal length of a zero-sum free sequence over G. Then d(G) ≥ d∗(G), and the standing conjecture is that equality holds for G = Cr n. We show that equality does not hold for C2 ⊕ Cr 2n, where n ≥ 3 is odd and r ≥ 4. This gives new information on the structure of extremal...

We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hi...

these are the positive integers that each have only two integer divisors (namely 1 and the number itself). By convention we do not take the number 1 to be prime. An immediate natural question, to which this notion leads, is already rather difficult: is the set of all the primes finite? In other words, can the above sequence of primes be continued indefinitely? The answer to this question was di...

Denote by f(k,m) the number of isomorphism classes of maximal intersecting k-uniform families of subsets of [m]. In this note we prove the existence of a constant f(k) such that f(k,m) ≤ f(k) for all values of m.