arXiv subjects

Maria Morariu

Publications and source records attributed to Maria Morariu.

2 recordsLinked to original sources

arXiv2026

A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds

This paper studies a subgroup of the mapping class group of an elliptically fibered $4$-manifold $π: M\to B$, inspired by number theory. The smooth Mordell-Weil group $\mathrm{MW}(π)$ is the group of isotopy classes of smooth sections of $π$. We construct a smooth analog of the Shioda-Tate isomorphism, identifying $\mathrm{MW(π)}$ with the quotient of $H^2(M;\mathbb{Z})$ by the trivial lattice of $π$. This shows that $\mathrm{MW}(π)$ can be computed explicitly from $H^2(M;\mathbb{Z})$. As an application, we show that the natural inclusion of the holomorphic Mordell-Weil group into the smooth one is an isomorphism if and only if $M$ is a rational elliptic surface. As another application, we show that $\mathrm{MW}(π)$ satisfies a strong version of Nielsen realization: any torsion element of $\mathrm{MW}(π)$ is represented by a holomorphic translation of $M$ of the same order.

math.GT↗

arXiv2026

The Smooth Narrow Mordell-Weil Group of Elliptically Fibered 4-Manifolds

For an elliptically fibered 4-manifold $π\colon M\to B$, we introduce a subgroup of the smooth mapping class group of $M$ with explicit geometric representatives: the smooth narrow Mordell-Weil group $MW_0(π)$. Leveraging Kodaira's classification of singular fibers, we construct a natural isomorphism between $MW_0(π)$ and the orthogonal complement of the trivial lattice in $H^2(M)$. This identification parallels its holomorphic counterpart. This paper generalizes work of Farb and Looijenga, who defined the smooth Mordell-Weil group and computed it for fibrations over a sphere with only nodal fibers. We give an explicit formula for the rank of $MW_0(π)$ depending only on the genus of the base curve and the types of singular fibers of $π$. As a corollary, we show that rational elliptic surfaces are the only elliptic surfaces with holomorphic and smooth Mordell-Weil groups of the same rank.

math.GT↗