arXiv subjects
Publications and source records attributed to Felipe Zingali Meira.
Let $k$ be a number field and $\mathcal{E}$ an elliptic curve defined over the function field $k(T)$ given by an equation of the form $y^2 = a_3x^3 + a_2x^2 + a_1x + a_0$, where $a_i \in k[T]$ and $deg(a_i) \leq 2$. We explore the conic bundle structure over the $x$-line to obtain lower and upper bounds for the Mordell--Weil rank of $\mathcal{E}(k(T))$.
We classify Jacobian elliptic fibrations on K3 surfaces with a non-symplectic automorphism $σ$ of order 3 according to the action of $σ$ on their fibres, building on work by Garbagnati and Salgado for non-symplectic involutions. We determine the possible reducible fibres types and give Weierstrass equations for Jacobian elliptic fibration which are preserved by $σ$. For a K3 surface $X$ with Picard number at least 12 and $σ$ acting trivially on $\NS X$, we apply the Kneser--Nishiyama method to find its Jacobian elliptic fibrations, and use our method to classify them in relation to every non-symplectic automorphism of order 3 in $\Aut X$.