## Determinantal IdealsDeterminantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are the ideal of the Veronese varieties, of the Segre varieties, and of the rational normal scrolls. Determinantal ideals are a central topic in both commutative algebra and algebraic geometry, and they also have numerous connections with invariant theory, representation theory, and combinatorics. Due to their important role, their study has attracted many researchers and has received considerable attention in the literature. In this book three crucial problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; and unobstructedness and dimension of families of standard determinantal ideals. Winner of the Ferran Sunyer i Balaguer Prize 2007. |

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### Contents

Background | 1 |

12 Determinantal ideals | 13 |

13 CIliaison and Gliaison | 21 |

CIliaison and Gliaison of Standard Determinantal Ideals | 29 |

21 CIliaison class of CohenMacaulay codimension 2 ideals | 30 |

22 CIliaison class of standard determinantal ideals | 33 |

23 Gliaison class of standard determinantal ideals | 41 |

Multiplicity Conjecture for Standard Determinantal Ideals | 45 |

Unobstructedness and Dimension of Families of Standard Determinantal Ideals | 62 |

41 Families of codimension 2 CohenMacaulay algebras | 65 |

42 Unobstructedness and dimension of families of determinantal schemes | 67 |

Determinantal Ideals Symmetric Determinantal Ideals and Open Problems | 105 |

51 Liaison class of determinantal and symmetric determinantal ideals | 106 |

52 The multiplicity conjecture for determinantal and symmetric determinantal ideals | 111 |

53 Unobstructedness and dimension of families of determinantal and symmetric determinantal ideals | 119 |

129 | |