## Algebra, Geometry and Their Interactions: International Conference Midwest Algebra, Geometry and Their Interactions: October 7-11, 2005, University of Notre Dame, Notre Dame, IndianaThis volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision. |

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### Contents

1 | |

Examples and counterexamples on the conjectured Hilbert function of multiple points | 13 |

Projectively full ideals in Noetherian rings a survey | 33 |

Cohomological degrees and the HomAB conjecture | 43 |

A minimal generating set for the first syzygies of a monomial ideal | 63 |

Lifting the determinantal property | 69 |

A survey | 91 |

Some finiteness properties of Lyubezniks Fmodules | 119 |

Ample vector bundles with sections vanishing on submanifolds of sectional genus three | 165 |

Finding all real points of a complex curve | 183 |

On the multiplicity conjecture | 207 |

Efficiently detecting torsion points and subtori | 215 |

Divisor class groups of graded hypersurfaces | 237 |

Irrelevant exceptional divisors for curves on a smooth surface | 245 |

Variation of hyperplane sections | 255 |

Jet schemes of determinantal varieties | 261 |

Minimal homogeneous liaison and licci ideals | 129 |

Unobstructedness and dimension of families of codimension 3 ACM algebras | 141 |

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### Common terms and phrases

ACM scheme algebraic algorithm ample vector bundle arithmetically Cohen–Macaulay assume boundary points char(k codimension complete intersection compute conjecture Corollary critical configurations defined deflation degg degree degree matrix denote dim(x dimension divisor class group edge ideals exact sequence example exceptional divisors facet ideals finite formula free resolution Gorenstein graded Betti numbers Hence Hilbert function homogeneous regular sequence HPTS(d hyperplane section hypersurface IA/B irreducible component isomorphic jet schemes jumping numbers Lemma line bundle m-primary Math maximal minors minimal free resolution minimally homogeneously licci module monomial monomial ideal Moreover morphism Noetherian ring obtain Pic(X positive integer prime projectively full PROOF prove quadric quotient R-module rational normal curve reconstruction Rees valuation ring REMARK root of unity saturated ideal simplicial complex singular smooth square-free standard determinantal scheme submaximal minors subscheme surjective symmetric matrix syzygies Theorem 3.1 torsion points vanishes vertex X C P zero