scholarly journals Foliations of multiprojective spaces and a conjecture of Bernstein and Lunts

2011 ◽  
Vol 363 (04) ◽  
pp. 2125-2125 ◽  
Author(s):  
S. C. Coutinho
Keyword(s):  
Multiprojective Spaces

scholarly journals WEAKLY UNIFORM RANK TWO VECTOR BUNDLES ON MULTIPROJECTIVE SPACES

2011 ◽  
Vol 84 (2) ◽  
pp. 255-260
Author(s):  
EDOARDO BALLICO ◽  
FRANCESCO MALASPINA
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Splitting Type ◽  
Multiprojective Spaces

AbstractHere we classify the weakly uniform rank two vector bundles on multiprojective spaces. Moreover, we show that every rank r>2 weakly uniform vector bundle with splitting type a1,1=⋯=ar,s=0 is trivial and every rank r>2 uniform vector bundle with splitting type a1>⋯>ar splits.

Special arrangements of lines: Codimension 2 ACM varieties in ℙ1 × ℙ1 × ℙ1

2019 ◽  
Vol 18 (04) ◽  
pp. 1950073 ◽  
Author(s):  
Giuseppe Favacchio ◽  
Elena Guardo ◽  
Beatrice Picone
Keyword(s):  
Point Of View ◽  
Arrangements Of Lines ◽  
Multiprojective Spaces ◽  
Combinatorial Algebra

In this paper, we investigate special arrangements of lines in multiprojective spaces. In particular, we characterize codimension 2 arithmetically Cohen–Macaulay (ACM) varieties in [Formula: see text], called varieties of lines. We also describe their ACM property from a combinatorial algebra point of view.

scholarly journals Multiprojective spaces and the arithmetically Cohen–Macaulay property

2018 ◽  
Vol 166 (3) ◽  
pp. 583-597 ◽  
Author(s):  
GIUSEPPE FAVACCHIO ◽  
JUAN MIGLIORE
Keyword(s):  
Ambient Space ◽  
Inclusion Property ◽  
New Construction ◽  
Multiprojective Spaces

AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.

scholarly journals Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze

2013 ◽  
Vol 46 (4) ◽  
pp. 549-627 ◽  
Author(s):  
Carlos D’Andrea ◽  
Teresa Krick ◽  
Martín Sombra
Keyword(s):  
Multiprojective Spaces

scholarly journals Lelong numbers of bidegree (1, 1) currents on multiprojective spaces

2019 ◽  
Vol 295 (3-4) ◽  
pp. 1569-1582
Author(s):  
Dan Coman ◽  
James Heffers
Keyword(s):  
Lelong Numbers ◽  
Multiprojective Spaces
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