Divisors

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title: Divisors permalink: wiki/Divisors/ layout: wiki

The following things are already done:

• type Divisor
• divisor from pair of ideals, from ideal
• normalForm
• globalSections
• linear Equivalence
• effective
• caonicalDivisor
• lineBundleFromDivisor

These things should be done:

• type DivisorClass: describes a divisor up to linear equivalence. Operations for this type are needed as well
• Linebundles: switch back and forth between linebundles (sheafs) and divisors
• degree: degree of divisors
• computation of intersection numbers: compute intersection numbers
• Kodaira-dimension compute the Kodaira-dimension of a nonsingular projective variety
• Ampleness: Check if a divisor is (very) ample
• very ambitious: Divisor class group: find out something about the divisor class group of a given variety

Note:

• The divisors in NormalToricVarieties will be implemented as type ToricDivisor which will for now be completely different from type Divisor