Corrado Segre and nodal cubic threefolds
Igor Dolgachev
TL;DR
This paper reviews Corrado Segre's work on nodal cubic threefolds, focusing on 6- and 10-nodal cases, and explores related algebraic geometry concepts like Fano surfaces and conic bundles.
Contribution
It provides a comprehensive review of Segre's contributions to the understanding of nodal cubic threefolds and discusses recent developments in the field.
Findings
Analysis of Fano surfaces associated with nodal cubics
Description of conic bundle structures on these threefolds
Connection to current research in algebraic geometry
Abstract
We discuss the work of Corrado Segre on nodal cubic hypersurfaces with emphasis on the cases of 6-nodal and 10-nodal cubics. In particular, we discuss the Fano surface of lines and conic bundle structures on such threefolds. We review some of the current research in algebraic geometry related to Segre's work.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Homotopy and Cohomology in Algebraic Topology