Flips and the Hilbert scheme over an exterior algebra. (English) Zbl 1128.14006
Let \(K\) be an infinite field and let \(E\) be the exterior algebra over \(K\). In the paper under review the authors study the tangent space at a monomial point \(M\) in the Hilbert scheme, that parameterizes all ideals with the same Hibert function as \(M\) over \(E\). They introduce the notion of flips and show that the basic flips form a basis of the tangent space at \(M\). This implies that the tangent space at \(M\) has a basis consisting of directions tangent to deformations built using Gröbner basis.
Reviewer: Anargyros Katsabekis (Nicosia)
MSC:
| 14D15 | Formal methods and deformations in algebraic geometry |
| 14E05 | Rational and birational maps |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 13F55 | Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes |
Software:
Macaulay2References:
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