Details:
Title  Upgraded methods for the effective computation of marked schemes on a strongly stable ideal  Author(s)  Cristina Bertone, Francesca Cioffi, Paolo Lella, margherita Roggero  Type  Article in Journal  Abstract  Let J ⊂ S = K [ x 0 , … , x n ] be a monomial strongly stable ideal. The collection M f ( J ) of the homogeneous polynomial ideals I, such that the monomials outside J form a Kvector basis of S / I , is called a Jmarked family. It can be endowed with a structure of affine scheme, called a Jmarked scheme. For special ideals J, Jmarked schemes provide an open cover of the Hilbert scheme H ilb p ( t ) n , where p ( t ) is the Hilbert polynomial of S / J . Those ideals more suitable to this aim are the mtruncation ideals J ̲ ⩾ m generated by the monomials of degree ⩾m in a saturated strongly stable monomial ideal J ̲ . Exploiting a characterization of the ideals in M f ( J ̲ ⩾ m ) in terms of a Buchbergerlike criterion, we compute the equations defining the J ̲ ⩾ m marked scheme by a new reduction relation, called superminimal reduction, and obtain an embedding of M f ( J ̲ ⩾ m ) in an affine space of low dimension. In this setting, explicit computations are achievable in many nontrivial cases. Moreover, for every m, we give a closed embedding ϕ m : M f ( J ̲ ⩾ m ) ↪ M f ( J ̲ ⩾ m + 1 ) , characterize those ϕ m that are isomorphisms in terms of the monomial basis of J ̲ , especially we characterize the minimum integer m 0 such that ϕ m is an isomorphism for every m ⩾ m 0 .  Keywords  Hilbert scheme, Strongly stable ideal, Polynomial reduction relation  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717112001241 
Language  English  Journal  Journal of Symbolic Computation  Volume  50  Number  0  Pages  263  290  Year  2013  Edition  0  Translation 
No  Refereed 
No 
