scholarly journals Base loci of linear systems and the Waring problem

2008 ◽  
Vol 137 (01) ◽  
pp. 91-98 ◽  
Author(s):  
Massimiliano Mella
Keyword(s):  
Linear Systems ◽  
Waring Problem ◽  
Base Loci

scholarly journals Homological Projective Duality for Linear Systems with Base Locus

2018 ◽  
Vol 2020 (21) ◽  
pp. 7829-7856 ◽  
Author(s):  
Francesca Carocci ◽  
Zak Turčinović
Keyword(s):  
Linear Systems ◽  
Dual Pair ◽  
Resolution Of Singularities ◽  
Smooth Variety ◽  
Rational Singularities ◽  
Base Locus ◽  
Projective Duality ◽  
Blowing Up ◽  
Linear Sections ◽  
Base Loci

Abstract We show how blowing up varieties in base loci of linear systems gives a procedure for creating new homological projective duals from old. Starting with a homological projective (HP) dual pair $X,Y$ and smooth orthogonal linear sections $X_L,Y_L$, we prove that the blowup of $X$ in $X_L$ is naturally HP dual to $Y_L$. The result also holds true when $Y$ is a noncommutative variety or just a category. We extend the result to the case where the base locus $X_L$ is a multiple of a smooth variety and the universal hyperplane has rational singularities; here the HP dual is a weakly crepant categorical resolution of singularities of $Y_L$. Finally we give examples where, starting with a noncommutative $Y$, the above process nevertheless gives geometric HP duals.

Uniruledness of stable base loci of adjoint linear systems via Mori theory

2013 ◽  
Vol 275 (1-2) ◽  
pp. 499-507 ◽  
Author(s):  
Sébastien Boucksom ◽  
Amaël Broustet ◽  
Gianluca Pacienza
Keyword(s):  
Linear Systems ◽  
Mori Theory ◽  
Base Loci

Linear systems with removable base loci

2000 ◽  
Vol 28 (12) ◽  
pp. 5931-5934 ◽  
Author(s):  
Lawrence Ein
Keyword(s):  
Linear Systems ◽  
Base Loci
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