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math.AG2005★ 1 cited
Relative Beilinson Monad and Direct Image for Families of Coherent Sheaves
David Eisenbud, Frank-Olaf Schreyer
The higher direct image complex of a coherent sheaf (or finite complex of coherent sheaves) under a projective morphism is a fundamental construction that can be defined via a Cech…
math.AG2004★ 3 cited
Restricting linear syzygies: algebra and geometry
David Eisenbud, Mark Green, Klaus Hulek +1
In this paper we derive geometric consequences from the presence of a long strand of linear syzygies in the minimal free resolution of a closed scheme in projective space whose hom…
math.AG2004
Small schemes and varieties of minimal degree
David Eisenbud, Mark Green, Klaus Hulek +1
We prove that if X is any 2-regular projective scheme (in the sense of Castelnuovo-Mumford) then X is "small". This means that if L is a linear space and Y:= L\cap X is finite, the…