AbstractSheaf -- the class of all abstract sheaves

Description

A virtual abstract sheaf over an abstract variety $X$ is specified by its total Chern character.

Functions and methods returning an abstract sheaf :

- AbstractSheaf -- negation of an abstract sheaf
AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
AbstractSheaf * ZZ -- see AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
AbstractSheaf ** AbstractSheaf -- see AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
QQ * AbstractSheaf -- see AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
ZZ * AbstractSheaf -- see AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf + QQ -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf + RingElement -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf + ZZ -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf ++ AbstractSheaf -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf ++ QQ -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf ++ RingElement -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf ++ ZZ -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
QQ + AbstractSheaf -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
QQ ++ AbstractSheaf -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
RingElement + AbstractSheaf -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
RingElement ++ AbstractSheaf -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
ZZ + AbstractSheaf -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
ZZ ++ AbstractSheaf -- see AbstractSheaf + AbstractSheaf -- (direct) sum of two abstract sheaves
AbstractSheaf - AbstractSheaf -- difference of two abstract sheaves
AbstractSheaf - QQ -- see AbstractSheaf - AbstractSheaf -- difference of two abstract sheaves
AbstractSheaf - RingElement -- see AbstractSheaf - AbstractSheaf -- difference of two abstract sheaves
AbstractSheaf - ZZ -- see AbstractSheaf - AbstractSheaf -- difference of two abstract sheaves
QQ - AbstractSheaf -- see AbstractSheaf - AbstractSheaf -- difference of two abstract sheaves
RingElement - AbstractSheaf -- see AbstractSheaf - AbstractSheaf -- difference of two abstract sheaves
ZZ - AbstractSheaf -- see AbstractSheaf - AbstractSheaf -- difference of two abstract sheaves
AbstractSheaf ^ ZZ -- power of an abstract sheaf
AbstractSheaf ^** QQ -- see AbstractSheaf ^** RingElement -- tensor power of an abstract sheaf
AbstractSheaf ^** RingElement -- tensor power of an abstract sheaf
AbstractSheaf ^** ZZ -- see AbstractSheaf ^** RingElement -- tensor power of an abstract sheaf
AbstractSheaf QQ -- see AbstractSheaf RingElement -- twist by a divisor class
AbstractSheaf RingElement -- twist by a divisor class
AbstractSheaf ZZ -- see AbstractSheaf RingElement -- twist by a divisor class
OO RingElement -- see AbstractSheaf RingElement -- twist by a divisor class
abstractSheaf -- see abstractSheaf(AbstractVariety,RingElement) -- make an abstract sheaf
adams(ZZ,AbstractSheaf) -- compute Adams operations
cotangentBundle -- get the cotangent bundle
determinant(AbstractSheaf) -- determinant of an abstract sheaf
dual(AbstractSheaf) -- the dual of an abstract sheaf
exteriorPower(AbstractSheaf) -- alternating sum of exterior powers
exteriorPower(ZZ,AbstractSheaf)
Hom(AbstractSheaf,AbstractSheaf) -- Hom between abstract sheaves
OO _ AbstractVariety -- the structure sheaf of an abstract variety
OO _ RingElement -- the abstract structure sheaf of a divisor class
schur -- see schur(List,AbstractSheaf) -- apply a Schur functor to an abstract sheaf
symmetricPower(RingElement,AbstractSheaf) -- symmetric power of an abstract sheaf
tangentBundle -- get the tangent bundle

Methods that use an abstract sheaf :

AbstractSheaf * QQ -- see AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
AbstractSheaf * RingElement -- see AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
RingElement * AbstractSheaf -- see AbstractSheaf * AbstractSheaf -- (tensor) product of two abstract sheaves
ch(AbstractSheaf) -- total Chern character of an abstract sheaf
ch(ZZ,AbstractSheaf) -- the i-th Chern character of an abstract sheaf
chern(AbstractSheaf) -- compute the total Chern class of a sheaf
chern(ZZ,AbstractSheaf) -- compute a Chern class of a sheaf
chern(ZZ,ZZ,AbstractSheaf) -- compute several Chern classes of an abstract sheaf
chi(AbstractSheaf) -- compute the Euler characteristic of an abstract sheaf
ctop(AbstractSheaf) -- the top Chern class of an abstract sheaf
degeneracyLocus(ZZ,AbstractSheaf,AbstractSheaf)
degeneracyLocus2(ZZ,AbstractSheaf,AbstractSheaf)
flagBundle(List,AbstractSheaf) -- see flagBundle -- make a flag bundle
incidenceCorrespondence(List,AbstractSheaf) -- build containment correspondence between two Grassmannians
kernelBundle(ZZ,AbstractSheaf,AbstractSheaf)
map(FlagBundle,AbstractVariety,AbstractSheaf) -- maps to projective bundles
projectiveBundle(AbstractSheaf) -- see projectiveBundle -- make a projective bundle from an abstract sheaf
projectiveBundle'(AbstractSheaf) -- see projectiveBundle' -- make a projective bundle from an abstract sheaf
rank(AbstractSheaf)
schur(List,AbstractSheaf) -- apply a Schur functor to an abstract sheaf
sectionZeroLocus(AbstractSheaf)
segre(AbstractSheaf) -- compute the total Segre class of a sheaf
segre(ZZ,AbstractSheaf) -- compute a Segre class of a sheaf
todd(AbstractSheaf) -- see todd -- compute the Todd class of an abstract sheaf, variety, map
variety(AbstractSheaf) -- the variety of an abstract sheaf

For the programmer

The object AbstractSheaf is a type, with ancestor classes HashTable < Thing.