Rational points on Del Pezzo surfaces of degree four
نویسندگان
چکیده
We study the distribution of Brauer group and frequency Brauer–Manin obstruction to Hasse principle weak approximation in a family smooth del Pezzo surfaces degree four over rationals.
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 کاملOn the Arithmetic of Del Pezzo Surfaces of Degree 2
Del Pezzo surfaces are smooth projective surfaces, isomorphic over the algebraic closure of the base ,eld to P P or the blow-up of P in up to eight points in general position. In the latter case the del Pezzo surface has degree equal to 9 minus the number of points in the blow-up. The arithmetic of del Pezzo surfaces over number ,elds is an active area of investigation. It is known that the Has...
متن کاملOn the unirationality of del Pezzo surfaces of degree 2
Among geometrically rational surfaces, del Pezzo surfaces of degree 2 over a field k containing at least one point are arguably the simplest that are not known to be unirational over k. Looking for k-rational curves on these surfaces, we extend some earlier work of Manin on this subject. We then focus on the case where k is a finite field, where we show that all except possibly three explicit d...
متن کاملOn the Arithmetic of Del Pezzo Surfaces of Degree
— We study the arithmetic of certain Del Pezzo surfaces of degree 2. We produce examples of Brauer-Manin obstruction to the Hasse principle, coming from 2and 4-torsion elements in the Brauer group.
متن کاملOn the Moduli of Degree 4 Del Pezzo Surfaces
We study irreducibility of families of degree 4 Del Pezzo surface fibrations over curves.
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: International Journal of Number Theory
سال: 2022
ISSN: ['1793-7310', '1793-0421']
DOI: https://doi.org/10.1142/s179304212250107x