Arithmetic of the moduli of semistable elliptic surfaces

25 Apr 2019 Han Changho Park Jun-Yong

We prove a new sharp asymptotic with the lower order term of zeroth order on $\mathcal{Z}_{\mathbb{F}_q(t)}(\mathcal{B})$ for counting the semistable elliptic curves over $\mathbb{F}_q(t)$ by the bounded height of discriminant $\Delta(X)$. The precise count is acquired by considering the moduli of nonsingular semistable elliptic fibrations over $\mathbb{P}^{1}$, also known as semistable elliptic surfaces, with $12n$ nodal singular fibers and a distinguished section... (read more)

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Categories

• ALGEBRAIC GEOMETRY
• ALGEBRAIC TOPOLOGY
• NUMBER THEORY
• SYMPLECTIC GEOMETRY