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Macaulay2 web site
Schubert2
::
AbstractSheaf
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)
-- exterior power
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)
-- compute the rank
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
.