Segre embeddings and finite semifields
نویسندگان
چکیده
منابع مشابه
Segre embeddings and finite semifields
Each embedded product space PG(n, q)×PG(n, q) in an (n2 +n− 1)-dimensional projective space is obtained by projecting the Segre variety Sn,n,q from an n-subspace δ skew with its first secant variety. On the other hand, when δ is skew with the (n − 1)-th secant variety, it determines a semifield of order qn+1 whose center contains Fq. A relationship arises between a particular class of embedding...
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In [2] a geometric construction was given of a finite semifield from a certain configuration of two subspaces with respect to a Desarguesian spread in a finite-dimensional vector space over a finite field. Moreover, it was proved that any finite semifield can be obtained in this way. In [7] we proved that the configuration needed for the geometric construction given in [2] for finite semifields...
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We study the syzygies of the ideals of the Segre embeddings. Let d ∈ N, d ≥ 3; we prove that the line bundle O(1, ..., 1) on the P 1 × ....× P 1 (d copies) satisfies Property Np of GreenLazarsfeld if and only if p ≤ 3. Besides we prove that if we have a projective variety not satisfying Property Np for some p, then the product of it with any other projective variety does not satisfy Property Np...
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Monomial ideals and toric rings are closely related. By consider a Grobner basis we can always associated to any ideal I in a polynomial ring a monomial ideal in≺I, in some special situations the monomial ideal in≺I is square free. On the other hand given any monomial ideal I of a polynomial ring S, we can define the toric K[I] ⊂ S. In this paper we will study toric rings defined by Segre embed...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2014
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2013.07.005