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Kazuki Utsumi

Publications and source records attributed to Kazuki Utsumi.

5 recordsLinked to original sources
arXiv2026

Singular fibers of elliptic fibrations on normal $K3$ surfaces

We study singular fibers of elliptic fibrations on normal \(K3\) surfaces. For a normal \(K3\) surface \(Y\) with minimal resolution \(ν\colon X \to Y\), we describe singular fibers on \(Y\) in terms of contractions of suitable ADE configurations of \((-2)\)-curves in singular fibers on \(X\). We determine ADE configurations occurring in singular fibers and describe fibers obtained after contraction. As a consequence, we obtain a description of singular fibers of elliptic fibrations on normal \(K3\) surfaces.

math.AG↗
arXiv2023

The Mordell-Weil lattice of an Inose surface arising from isogenous elliptic curves

An elliptic K3 surface having two $II^{*}$ fibers is called the Inose surface. In this paper, we give a method to find a rational section of an Inose surface corresponding to an isogeny of general degree between two elliptic curves. In particular, we show examples of bases of the Mordell-Weil lattices of Inose surfaces arising from isogenies of degrees 5 and 6.

math.AG↗
arXiv2018

Mordell-Weil lattice of Inose's Elliptic $K3$ surface arising from the product of 3-isogenous elliptic curves

From the product of two elliptic curves, Shioda and Inose constructed an elliptic $K3$ surface having two $\mathrm{II}^*$ fibers. Its Mordell-Weil lattice structure depends on the morphisms between the two elliptic curves. In this paper, we give a method of writing down generators of the Mordell-Weil lattice of such elliptic surfaces when two elliptic curves are $3$-isogenous. In particular, we obtain a basis of the Mordell-Weil lattice for the singular $K3$ surfaces $X_{[3,3,3]}$, $X_{[3,2,3]}$ and $X_{[3,0,3]}$.

math.AG↗