Index 225 uniqueness of –, 131 point derivation, 79 principal open set, 9 projective closure of an aﬃne variety, 23 variety, 20 quasi-projective variety, 32 quotient categorical –, 69 Chevalley –, 69 radical ideal, 4 of an ideal, 4 rational function, 10 domain of definition of a –, 10 regular –, 10 rational map, 12,13 domain of definition of a –, 12 dominant –, 13 regular function on a projective variety, 23 regular map, 12 regular singular point, 165 Riccati equation, 163 right convolution, 80 ring of constants, 123 of linear differential operators, 125 Ritt algebra, 133 semi-invariant of an algebraic group, 67 semisimple endomorphism, 86 semisimple part, 89 sheaf of functions, 17 simple point, 44 solvable group, 93 solvable Lie algebra, 79 special linear group, 56 special unitary group, 105 subprevariety, 28 subvariety, 32 tangent space to a variety at a point, 42 triangularizable set of matrices, 90 unipotent endomorphism, 87 unipotent part, 89 unitary matrix, 105 upper triangular group, 56 upper triangular unipotent group, 56 variety abstract aﬃne –, 18 nonsingular –, 44 weight of a semi-invariant, 67 wro´ nskian (determinant), 126 Zariski’s main theorem, 42 Zariski topology, 4 Zariski topology of the projective space, 21

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