## Methods of Algebraic Geometry:All three volumes of Hodge and Pedoe's classic work have now been reissued. Together, these books give an insight into algebraic geometry that is unique and unsurpassed. |

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### Contents

BOOK III GENERAL THEORY OF ALGEBRAICVARIETIES IN PROJECTIVE SPACE | 1 |

BOOK IVQUADRICS AND GRASSMANN VARIETIES | 201 |

BIBLIOGRAPHICAL NOTES | 388 |

390 | |

391 | |

### Common terms and phrases

absolutely irreducible algebraic extension algebraic system algebraic variety algebraically independent Cayley form coeﬂicients column conjugate consider contains coordinate system d-space deduce deﬁnition degree g elementary divisors elements equivalence F(uo ﬁnd ﬁnite number ﬁrst follows given Grassmann coordinates ground ﬁeld Hence homogeneous image-variety independent indeterminates integers intersect simply irreducible components irreducible system irreducible variety join Lemma linear space matrix meet non-singular quadric normal problem normalised object-variety obtain order g orthogonal orthogonal matrix point of Sn polar prime polar space polynomial primal projective transformation proper specialisation properties Q and Q Qn_1 satisﬁes the equations Schubert variety Segre symbol set of equations simple point singular skew-symmetric matrix solution space of dimension standard power-products subvariety suﬂicient suppose system of varieties tangent prime tangent space vanishes variety in Sn variety of dimension vertex virtual varieties zero