geometry, a relative effective Cartier divisor is roughly a family of effective Cartier divisors. Precisely, an effective Cartier divisor in a scheme...

divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors...

points, the notion of 'divisor' is inherently ambiguous (Cartier divisors, Weil divisors: see divisor (algebraic geometry)). The definition in that case is...

f′-ample sheaf on X′ which does not descend to X. fpqc morphism Relative effective Cartier divisor, an example of a flat morphism Degeneration (algebraic geometry)...

{\displaystyle c_{1}(L)} means the associated Cartier divisor (defined up to linear equivalence), the divisor of any nonzero rational section of L. On a...

graded Lie algebra Kodaira–Spencer map Frobenius splitting Relative effective Cartier divisor M. Artin, Lectures on Deformations of Singularities – Tata...

and the set of effective Weil divisors on X that are linearly equivalent to D. The same definition is used if D is a Cartier divisor on a complete variety...

(in the sense of category theory) way to turn a subvariety into a Cartier divisor. A blowup can also be called monoidal transformation, locally quadratic...

is an effective procedure for assigning a height function to any divisor on smooth projective variety over a number field (or to Cartier divisors on non-smooth...

dimension. Let D ↪ X {\displaystyle D\hookrightarrow X} be an effective Cartier divisor. Then the normal bundle to it (or equivalently the normal cone...

turbulence during the 1970s. Scharlau 2008. Cartier et al. 2007, p. 7. Cartier 2004. Douroux 2012. Cartier 2004, p. 10, footnote 12. Kleinert 2007. Jackson...

exceptional divisor E := π − 1 ( Z ) ↪ X ~ {\displaystyle E:=\pi ^{-1}(Z)\hookrightarrow {\widetilde {X}}} is an effective Cartier divisor and the normal...

length r. A regular embedding of codimension one is precisely an effective Cartier divisor. For example, if X and Y are smooth over a scheme S and if i is...

is a Fano variety with ample Q {\displaystyle \mathbb {Q} } -Cartier anticanonical divisor and at worst Kawamata log terminal (klt) singularities. The...