Definitions
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Special types of varieties:
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What is a Fano variety?
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What is a del Pezzo surface?
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What is a ruled variety?
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What is a uniruled variety?
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What is an elliptic curve?
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What is a hyperelliptic curve?
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What is the Jacobian of a curve?
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What is the special divisor?
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What is the ramification divisor?
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What is the Frobenius map?
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What is an elliptic curve?
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What is the \(j\) invariant?
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What is the Jacobian variety?
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What is an elliptic function?
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What is the Hasse invariant?
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What is the canonical embedding?
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What is an algebraic curve?
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What is the genus of a curve? The geometric genus? The arithmetic genus?
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What is the dual curve?
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What is the resultant?
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What is the Kodaira dimension?
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What is the Todd genus?
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What is a minimal model of a smooth projective variety?
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What is an elliptic fibration?
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Types of surfaces:
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An Enriques surface?
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A K3 surface?
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A hyperelliptic surface?
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An abelian surface?
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An elliptic surface?
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What is an abelian variety?
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What is a log resolution?
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What is a rational curve?
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What is a stable map?
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What is a reducible curve?
Results
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What is the Riemann-Roch theorem for curves?
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What is Hurwitz’s theorem?
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What is the classification of curves in \({\mathbb{P}}^3\)?
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What is the Riemann-Hurwitz formula?
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What is the genus formula for plane curves?