A Note on Severi Varieties of Nodal Curves on Enriques Surfaces

We prove that the negativity of Shimura curves on quaternionic Shimura surfaces of Hilbert modular type is bounded and that there exist only finitely many negative curves.. This

The Hilbert scheme of rational, smooth and irreducible curves C of degree d on a general quintic threefold in P 4 is finite, nonempty and reduced, so each curve is embedded with

As it turns out, the most difficult point will be to show that a tetragonal curve of genus g ≥ 7 lying on an Enriques surface and general in its linear system, in its

The two main purposes of this paper are (1) to classify all cases of exceptional curves on Del Pezzo surfaces and (2) to study the gonality and Clifford index of linearly

We assume in fact that the surfaces in B and nodal curves on them possess good semistable degenerations with limiting surfaces that are reducible in two components (the more

We prove that the negativity of Shimura curves on quaternionic Shimura surfaces of Hilbert modular type is bounded and that there exist only finitely many negative Shimura curves..

The curves on S in Theorem 0.1 determine a family of rational curves in Hilb k (S) of dimension 2(k − 1), which is the expected dimension of any family of rational curves on

Indeed, this technique proved useful in many contexts, such as Voisin’s proof of Green’s Conjecture for a general curve of any given genus [48, 49], higher rank Brill–Noether