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Week
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Topics
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Study Metarials
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1
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Affine algebraic sets, the Hilbert basis theorem
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R1-Chapter 1
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2
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Ideal-algebraic set correspondence, irreducibility
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R1-Chapter 1
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3
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Affine varieties, coordinate rings
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R1-Chapter 2
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4
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Polynomial maps, rational functions
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R1-Chapter 2
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5
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Local rings, multiplicities
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R1-Chapter 3
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6
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Tangent lines, intersection numbers
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R1-Chapter 3
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7
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Projective spaces, projective sets
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R1-Chapter 4
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8
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Projective varieties, multiprojective spaces
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R1-Chapter 4
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9
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Curves in projective plane
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R1-Chapter 5
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10
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Linear systems of curves, Bezout`s theorem
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R1-Chapter 5
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11
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Zariski topology, algebraic function fields, dimension
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R1-Chapter 6
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12
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Resolution of singularities, blowing up, nonsingular models
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R1-Chapter 7
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13
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Divisors, differential, canonical divisors
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R1-Chapter 8
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14
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Riemann-Roch theorem and its applications
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R1-Chapter 8
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