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Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs
Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs
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Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs
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Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs
Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs

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Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs
Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs
Journal Article

Moduli spaces of 6×6\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6\\hspace{1.111pt}{\\times }\\hspace{1.111pt}6$$\\end{document} skew matrices of linear forms on P4\\documentclass12pt{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs

2024
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Overview
It is well known that every smooth cubic threefold is the zero locus of the Pfaffian of a 6×6 skew-symmetric matrix of linear forms in P4 . To compactify the space of such Pfaffian representations of a given cubic and to study the construction in families for singular or reducible cubics as well as, it is thus natural to consider the incidence correspondence of Pfaffian representations inside the product of the space of semistable skew-symmetric 6×6 matrices of linear forms in P4 and the space of cubics. Here we describe concretely the irreducible component of this incidence correspondence dominating the space of skew matrices.
Publisher
Springer Nature B.V