Geodesic
Gröbner geometry of Schubert polynomials
Allen Knutson1 ; Ezra Miller2
1Department of Mathematics, University of California, Berkeley, CA 94720, United States
2School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States
Annals of mathematics, Tome 161 (2005) no. 3, pp. 1245-1318
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Given a permutation $w \in S_n$, we consider a determinantal ideal $I_w$ whose generators are certain minors in the generic $n \times n$ matrix (filled with independent variables). Using ‘multidegrees’ as simple algebraic substitutes for torus-equivariant cohomology classes on vector spaces, our main theorems describe, for each ideal $I_w$:

DOI : 10.4007/annals.2005.161.1245

Allen Knutson  1   ; Ezra Miller  2

1 Department of Mathematics, University of California, Berkeley, CA 94720, United States
2 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States 
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Allen Knutson; Ezra Miller. Gröbner geometry of Schubert polynomials. Annals of mathematics, Tome 161 (2005) no. 3, pp. 1245-1318. doi: 10.4007/annals.2005.161.1245

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