Abstract. Let C be a non-hyperelliptic algebraic curve. It is known that its canonical image is the intersection of the quadrics that contain it, except when C is trigonal (that is, it has a linear system of degree 3 and dimension 1) or isomorphic to a plane quintic (genus 6). In this context, we present a method to decide whether a given algebraic curve is trigonal, and in the affirmative case...

The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.

We prove development of type I singularities for a suitable concept of weak evolution in the context of the quintic focussing NLW on R3`1, for data near and “above” the ground state static solution.

In this paper we first characterize all quasi–homogeneous but non–homogeneous planar polynomial differential systems of degree five, and then among which we classify all the ones having a center at the origin. Finally we present the topological phase portrait of the systems having a center at the origin.

After Bershadsky-Cecotti-Ooguri-Vafa, we introduce an invariant of Calabi-Yau threefolds, which we call the BCOV invariant and which we obtain using analytic torsion. We give an explicit formula for the BCOV invariant as a function on the compactified moduli space, when it is isomorphic to a projective line. As a corollary, we prove the formula for the BCOV invariant of quintic mirror threefold...

We construct a hypersurface of degree 5 in projective space P(C) which contains exactly 23436 ordinary nodes and no further singularities. This limits the maximum number μ8(5) of ordinary nodes a hyperquintic in P(C) can have to 23436 ≤ μ8(5) ≤ 27876. Our method generalizes the approach by the 3 author for the construction of a quintic threefold with 130 nodes in an earlier paper.

Manin’s conjecture is proved for a split del Pezzo surface of degree 5 with a singularity of type A2.

We study conformal field theories for strings propagating on compact, seven-dimensional manifolds with G 2 holonomy. In particular, we describe the construction of rational examples of such models. We argue that analogues of Gepner models are to be constructed based not on N = 1 minimal models, but on Z 2 orbifolds of N = 2 models. In Z 2 orbifolds of Gepner models times a circle, it turns out ...

Let f(x) = x+ax+bx+cx ∈ Z[x] and consider the hypersurface of degree five given by the equation Vf : f(p) + f(q) = f(r) + f(s). Under the assumption b 6= 0 we show that there exists Q-unirational elliptic surface contained in Vf . If b = 0, a < 0 and −a 6≡ 2, 18, 34 (mod 48) then there exists Q-rational surface contained in Vf . Moreover, we prove that for each f of degree five there exists Q(i...