Abstract
We show that given integers N N , d d and n n such that N ≥ 2 , ( N , d , n ) {N\ge 2}, (N,d,n) ≠ ( 2 , 2 , 5 ) \ne (2,2,5) , and N + 1 ≤ n ≤ ( d + N N ) {N+1\le n\le \tbinom {d+N}{N}} , there is a family of n n monomials in K [ X 0 , … , X N ] K\left [X_0,\ldots ,X_N\right ] of degree d d such that their syzygy bundle is stable. Case N ≥ 3 {N\ge 3} was obtained independently by Coandǎ with a different choice of families of monomials. For ( N , d , n ) = ( 2 , 2 , 5 ) {(N,d,n)=(2,2,5)} , there are 5 5 monomials of degree 2 2 in K [ X 0 , X 1 , X 2 ] K\left [X_0,X_1,X_2\right ] such that their syzygy bundle is semistable.
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