Quartic spectrahedra
成果类型：
Article
署名作者：
Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd; Vinzant, Cynthia
署名单位：
University of Cambridge; University of Oslo; University of California System; University of California Berkeley; North Carolina State University
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-014-0844-3
发表日期：
2015
页码：
585-612
关键词：
摘要：
Quartic spectrahedra in 3-space form a semialgebraic set of dimension 24. This set is stratified by the location of the ten nodes of the corresponding real quartic surface. There are twenty maximal strata, identified recently by Degtyarev and Itenberg, via the global Torelli Theorem for real K3 surfaces. We here give a new proof that is self-contained and algorithmic. This involves extending Cayley's characterization of quartic symmetroids, by the property that the branch locus of the projection from a node consists of two cubic curves. This paper represents a first step towards the classification of all spectrahedra of a given degree and dimension.
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