Computing the lines of a smooth cubic surface
Hossein Movasati
TL;DR
This paper provides an explicit formula for the 27 lines on a smooth cubic surface close to the Fermat surface, using power series and Artinian Gorenstein rings.
Contribution
It introduces a new explicit formula involving convergent power series and Gorenstein rings for computing lines on cubic surfaces near the Fermat surface.
Findings
Explicit formula for lines near Fermat surface
Use of power series with sixth root of unity coefficients
Application of Artinian Gorenstein rings
Abstract
We give an explicit formula for the lines of a smooth cubic surface near the Fermat surface. Our formula involves convergent power series with coefficients in the extension of rational numbers with the sixth root of unity. Our main tool is the Artinian Gorenstein ring of socle two attached to such lines.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models