intersectionCohomology -- intersection cohomology of an irreducible affine variety

Synopsis

• Usage:

  IH I

  intersectionCohomology(I)

  IH^d I

  intersectionCohomology(d,I)

• Inputs:
  • I, an ideal, in the polynomial ring $R$
  • d, an integer, the degree
• Optional inputs:
  • Strategy => a string, default value Schreyer, see Dintegration(...,Strategy=>...)
  • LocCohomStrategy => a sequence, default value (Walther,), (String, String); see localCohom(...,Strategy=>...) and localCohom(...,LocStrategy=>...)
  • LocStrategy => a string, default value OTW, see IHmodule(...,LocStrategy=>...)
• Outputs:
  • a hash table, a table including the intersection cohomology groups of the irreducible variety Spec($R/I$),
  • a module, the intersection cohomology group in degree d

Description

i1 : R=QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x^2+y^3)

            3    2
o2 = ideal(y  + x )

o2 : Ideal of R

i3 : intersectionCohomology(I)

                      1
o3 = HashTable{0 => QQ }
               1 => 0

o3 : HashTable

Caveat