Complex Varieties of General Type Whose Canonical Systems Are Composed with Pencils
نویسنده
چکیده
Throughout this paper, most our notations and terminologies are standard within algebraic geometry except for the following which we are in favour of: := — definition; ∼lin — linear equivalence; ∼num — numerical equivalence. Let X be a complex nonsingular projective variety of general type with dimension d(d ≥ 2). Suppose dimΦ|KX |(X) = 1, we usually say that the canonical system |KX | is composed with a pencil. Taking possible blow-ups π : X ′ → X according to Hironaka such that g := Φ|KX | ◦ π is a morphism. We have the following commutative diagram: X ′ f −−−−→ C
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