Rational cuspidal curves on del-Pezzo surfaces
نویسندگان
چکیده
منابع مشابه
Rational Points on Certain Del Pezzo Surfaces of Degree One
Let f(z) = z +az + bz + cz+ d ∈ Z[z] and let us consider a del Pezzo surface of degree one given by the equation Ef : x 2 − y − f(z) = 0. In this note we prove that if the set of rational points on the curve Ea, b : Y 2 = X + 135(2a − 15)X − 1350(5a + 2b − 26) is infinite, then the set of rational points on the surface Ef is dense in the Zariski topology.
متن کاملCurves and Line Bundles on Del Pezzo Surfaces
We extend the results of Pareschi [Pa] on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees ≥ 2 to the case of Del Pezzo surfaces of degree 1, where we explicitly classify the cases where the gonality and Clifford index are not constant. We also classify all cases of exceptional curves on Del Pezzo surfaces, which turn...
متن کاملThe irreducibility of the spaces of rational curves on del Pezzo surfaces
Let X be a del Pezzo surface of degree d, and assume that X is general if d = 1. We prove that the spaces M0,0 ( X, β ) are either empty or irreducible, if (d, β) 6= (1,−KX). When (d, β) = (1,−KX) it is well known that M0,0 ( X, β ) consists of twelve reduced points.
متن کاملNonnormal Del Pezzo Surfaces
0.1 Throughout this paper, a del Pezzo surface is by definition a connected, 2-dimensional, projective k-scheme X,OX(1) that is Gorenstein and anticanonically polarised; in other words, X is Cohen–Macaulay, and the dualising sheaf is invertible and antiample: ωX ∼= OX(−1). For example, X = X3 ⊂ P 3 an arbitrary hypersurface of degree 3. Under extra conditions, del Pezzo surfaces are interesting...
متن کاملQuartic Del Pezzo Surfaces over Function Fields of Curves
The geometry of spaces of rational curves of low degree on Fano threefolds is a very active area of algebraic geometry. One of the main goals is to understand the Abel-Jacobi morphism from the base of a space of such curves to the intermediate Jacobian of the threefold. For instance, does a given space of curves dominate the intermediate Jacobian? If so, what are the fibers of this morphism? Do...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Singularities
سال: 2018
ISSN: 1949-2006
DOI: 10.5427/jsing.2018.17f