effective divisor造句

• Every semi-ample divisor is nef, but not every nef divisor is numerically equivalent to a semi-ample divisor, or even to an effective divisor.
• A complete linear system on " V " is defined as the set of all effective divisors linearly equivalent to some given divisor " D ".
• Where \ operatorname { Supp } denotes the support of a divisor, and the intersection is taken over all effective divisors D _ \ text { eff } in the linear system.
• In the function field case, a modulus is the same thing as an effective divisor, and in the number field case, a modulus can be considered as special form of Arakelov divisor.
• From the divisor linear equivalence / line bundle isomorphism principle, a Cartier divisor is linearly equivalent to an effective divisor if, and only if, its associated line bundle \ mathcal L ( D ) has non-zero global sections.
• Its interest in relation to the classical geometry of curves is that its points correspond to effective divisors on " C " of degree " n ", that is, formal sums of points with non-negative integer coefficients.
• Two collinear non-zero global sections have the same vanishing locus, and hence the projective space \ mathbb P \ Gamma ( X, \ mathcal L ( D ) ) over "'k "'identifies with the set of effective divisors linearly equivalent to D.
• He also described which points on " W " " g " & minus; 1 are non-singular : they correspond to the effective divisors " D " of degree " g " & minus; 1 with no associated meromorphic functions other than constants.
• Over the complex numbers the analytic subgroup underlying the generalized Jacobian can be described as follows . ( This does not always determine the algebraic structure as two non-isomorphic commutative algebraic groups may be isomorphic as analytic groups . ) Suppose that " C " is a curve with an effective divisor " m " with support " S ".
• It follows that " L " is nef, but no positive multiple of the first Chern class " c " 1 ( " L " ) is numerically equivalent to an effective divisor . ( The first Chern class is an isomorphism from the Picard group of line bundles on a variety " X " to the group of Cartier divisors modulo linear equivalence .)