## Abel-Jacobi Isogenies for Certain Types of Fano Threefolds |

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### Contents

INTRODUCTION 3 | v |

INFINITESIMAL STUDIES | 14 |

INFINITESIMAL ABELJACOBI MAPPINGS | 20 |

8 other sections not shown

### Common terms and phrases

2-plane Abel-Jacobi map Alb(Y algebraic base point bitangents bundle Chow cohomology cohomology sequence commutative diagram complete intersection conic consider containing curve of divisors curves of degree defined degenerate denotes dimension discriminant point divisor variety double cover equations equivalent exact sequence exactly fact Fano surface Fano varieties fibre fixed genus given gotten halves hence holds hyperflex hyperplane section identified induced infinitesimal intermediate Jacobian inverse image irreducible component isogeny isomorphism latter LEMMA linear sections linear system locus lying map F meeting morphism natural map notations NZ/Y parametrized pencil point of contact principally polarized proof PROPOSITION prove Prym variety quadrics quartic surface REMARK resp sheaf singular smooth complete smooth curve smooth plane septic Suppose surface F surface of divisors surjective Theorem theta characteristic theta divisor three quadrics tion twisted cubic vanishing variety of divisors vector space yields zero zijn