Very Ample Linear Systems on Blowings-Up at General Points of Projective Spaces

2002 ◽  
Vol 45 (3) ◽  
pp. 349-354 ◽  
Author(s):  
Marc Coppens
Keyword(s):  
Projective Space ◽  
Linear Systems ◽  
Exceptional Divisor ◽  
Closed Field ◽  
Invertible Sheaf ◽  
Algebraically Closed Field ◽  
Structure Sheaf ◽  
Blowing Up ◽  
Dimensional Projective Space ◽  
Ample Invertible Sheaf

AbstractLet Pn be the n-dimensional projective space over some algebraically closed field k of characteristic 0. For an integer t ≥ 3 consider the invertible sheaf O(t) on Pn (Serre twist of the structure sheaf). Let , the dimension of the space of global sections of O(t), and let k be an integer satisfying 0 < k ≤ N − (2n + 2). Let P1,…,Pk be general points on Pn and let π : X → Pn be the blowing-up of Pn at those points. Let Ei = π−1(Pi) with 1 ≤ i ≤ k be the exceptional divisor. Then M = π*(O(t)) ⊗ OX(−E1 — … — Ek) is a very ample invertible sheaf on X.

A COMINRES-QLP Method for Solving Complex Symmetric Linear Systems

2020 ◽  
Vol 140 (12) ◽  
pp. 832-841
Author(s):  
Lijun Liu ◽  
Kazuaki Sekiya ◽  
Masao Ogino ◽  
Koki Masui
Keyword(s):  
Linear Systems ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric
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