Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces

Free Download Varieties of Nodal Surfaces, Coding Theory and Discriminants of Cubic Hypersurfaces
English | 2026 | ISBN: 3032058988 | 220 Pages | PDF EPUB (True) | 24 MB
This research book deals with some classical problems of algebraic geometry, notably the problem about the maximal number of singularities that a nodal variety can have, and the problem about the description of the components of the Severi varieties of nodal surfaces. A complete solution is found for nodal quartic surfaces in 3-space and for nodal K3 surfaces. New striking results are found also for quintic and sextic surfaces. The main focus of the book is the relation of nodal surfaces with binary coding theory, introduced by Beauville: two codes are attached to a nodal projective surface, which are invariants of these components, and in some cases determine them.

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