Periods of elliptic surfaces with $p_g=q=1$
Philip Engel, Fran\c{c}ois Greer, Abigail Ward
TL;DR
This paper proves that the period mapping for certain elliptic surfaces over an elliptic curve with 12 nodal fibers is dominant and has degree greater than one, revealing new insights into their geometric properties.
Contribution
It establishes the dominance and degree of the period mapping for elliptic surfaces with specific singular fibers, advancing understanding of their moduli.
Findings
Period mapping is dominant for the specified elliptic surfaces.
The degree of the period mapping exceeds one.
Provides new results on the moduli of elliptic surfaces.
Abstract
We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with 12 nodal fibers, and that its degree is larger than 1.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Meromorphic and Entire Functions