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 modern research in algebraic geometry related to Segre’s work.
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Notes
- 1.
This fact was essentially known to Fano (1904a).
- 2.
To get expected degree 15 one has to add six lines here that come from a choice of one ruling in each exceptional divisor of the resolution \( X^{\prime} \to X \).
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Dolgachev, I. (2016). Corrado Segre and Nodal Cubic Threefolds. In: Casnati, G., Conte, A., Gatto, L., Giacardi, L., Marchisio, M., Verra, A. (eds) From Classical to Modern Algebraic Geometry. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-32994-9_11
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