A FRAMEWORK FOR TORSION THEORY COMPUTATIONS ON ELLIPTIC THREEFOLDS

We give a list of statements on the geometry of elliptic threefolds phrased only in the language of topology and homological algebra. Using only notions from topology and homological algebra, we recover existing results and prove new results on torsion pairs in the category of coherent sheaves on an elliptic threefold.

Mordell–Weil groups of elliptic threefolds and the Alexander module of plane curves

We establish a correspondence between the rank of Mordell–Weil group of the complex elliptic threefold associated with a plane curve 𝒞 ⊂ ℙAs a consequence we find a linear bound for the degree of the Alexander polynomial in terms of the degree of 𝒞 for curves with δ-essential singularities and in particular arbitrary ADE singularities.