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Virtual complete intersections in $$\mathbb{P}^1\times\mathbb{P}^1$$. (English) Zbl 1441.13031
Summary: The minimal free resolution of the coordinate ring of a complete intersection in projective space is a Koszul complex on a regular sequence. In the product of projective spaces $$\mathbb{P}^1\times\mathbb{P}^1$$, we investigate which sets of points have a virtual resolution that is a Koszul complex on a regular sequence. This paper provides conditions on sets of points; some of which guarantee the points have this property, and some of which guarantee the points do not have this property.
##### MSC:
 13D02 Syzygies, resolutions, complexes and commutative rings 14M25 Toric varieties, Newton polyhedra, Okounkov bodies
Macaulay2
Full Text:
##### References:
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