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demo2.m2
-- Here are some more demos based on examples from classic schubert, not from the Schubert manual, some with Schubert code in comments needsPackage "Schubert2" pt = base() -- # of elliptic cubics on a sextic 4 fold, a schubert-classic example from Rahul: -- Enumerative Geometry of Calabi-Yau 4-Folds -- Communications in Mathematical Physics -- Volume 281, Number 3 / August, 2008 -- Pages 621-653 -- Enumerative Geometry of Calabi-Yau 4-Folds -- A. Klemm and R. Pandharipande -- grass(3,6,c): Gc = flagBundle({3,3}, pt, VariableNames => {,c}) (Sc,Qc) = Gc.Bundles -- B:=Symm(3,Qc): B = symmetricPower_3 Qc -- Proj(X,dual(B),z): X = projectiveBundle'(dual B, VariableNames => {,{z}}) -- A:=Symm(6,Qc)-Symm(3,Qc)&@o(-z): A = symmetricPower_6 Qc - symmetricPower_3 Qc ** OO(-z) -- c18:=chern(rank(A),A): c18 = chern(rank A,A) -- lowerstar(X,c18): X.StructureMap_* c18 -- integral(Gc,%); integral oo assert( oo == 2734099200 ) -- Ans = 2734099200 integral chern A assert( oo == 2734099200 ) -- -- a similar example -- in P^4 ... what does this count? Gc = flagBundle({2,3}, pt, VariableNames => {,c}) (Sc,Qc) = Gc.Bundles B = symmetricPower_7 Qc X = projectiveBundle'(dual B, VariableNames => {,{z}}) A = symmetricPower_15 Qc - symmetricPower_3 Qc ** OO(-z) integral chern A assert( 99992296084705144978200 == oo)
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