map(FlagBundle,AbstractVarietyMap,List) -- make a map from an abstract variety to a flag bundle

Synopsis

• Function: map

• Usage:

  map(F,f,b)

  map(F,X,b)

• Inputs:
  • F, an abstract flag bundle, over a variety S, of the form $flagBundle(\{r_0, ..., r_{n-1}\},E)$, say, where $E$ is an abstract sheaf on $S$
  • an abstract variety map, f, an abstract variety map from a variety $X$, say, to $S$; or X, an abstract variety, with a structure map $f : X \rightarrow{} S$
  • b, a list, of the form $\{B_0,...B_{n-1}\}$ whose elements are abstract sheaves on X, with $rank B_i = r_i$, for each i. The sheaves should be effective in the sense that $c_j B_i = 0$ for $j > r_i$. The sum of the sheaves should equal $f^* E$; alternatively, one of them can be omitted and it will be deduced from the condition on the sum.
• Optional inputs:
  • Degree => ..., default value null, the value of this option is ignored
  • DegreeLift => ..., default value null, the value of this option is ignored
  • DegreeMap => ..., default value null, the value of this option is ignored
• Outputs:
  • an abstract variety map, the map of abstract varieties $g : X \rightarrow{} F$ over $S$ such that $g^* (E_{i+1}/E_i) = B_i$, for each i, where $0 = E_0 \subseteq{} E_1 \subseteq{} ... \subseteq{} E_n = p^* E$ is the tautological filtration on $F$, and where $p : F \rightarrow{} S$ is the structure map of $F$.

Description