scholarly journals On the arithmetic rank of certain Segre products

2005 ◽  
pp. 147-155 ◽  
Author(s):  
Anurag K. Singh ◽  
Uli Walther
Keyword(s):  
Arithmetic Rank

scholarly journals SYMBOLIC ANALYTIC SPREAD: UPPER BOUNDS AND APPLICATIONS

2020 ◽  
pp. 1-13
Author(s):  
Hailong Dao ◽  
Jonathan Montaño
Keyword(s):  
Complete Intersection ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Kodaira Dimension ◽  
Rate Of Growth ◽  
Symbolic Powers ◽  
Number Of Generators ◽  
Analytic Spread ◽  
General Systems ◽  
Arithmetic Rank

The symbolic analytic spread of an ideal $I$ is defined in terms of the rate of growth of the minimal number of generators of its symbolic powers. In this article, we find upper bounds for the symbolic analytic spread under certain conditions in terms of other invariants of $I$ . Our methods also work for more general systems of ideals. As applications, we provide bounds for the (local) Kodaira dimension of divisors, the arithmetic rank, and the Frobenius complexity. We also show sufficient conditions for an ideal to be a set-theoretic complete intersection.

scholarly journals Finiteness of Teichmüller Curves in Non-Arithmetic Rank 1 Orbit Closures

2017 ◽  
Vol 139 (6) ◽  
pp. 1449-1463 ◽  
Author(s):  
Erwan Lanneau ◽  
Duc-Manh Nguyen ◽  
Alex Wright
Keyword(s):  
Orbit Closures ◽  
Teichmuller Curves ◽  
Teichmüller Curves ◽  
Arithmetic Rank

ARITHMETIC RANK, COHOMOLOGICAL DIMENSION AND FILTER REGULAR SEQUENCES

2009 ◽  
Vol 08 (06) ◽  
pp. 855-862 ◽  
Author(s):  
ALI AKBAR MEHRVARZ ◽  
KAMAL BAHMANPOUR ◽  
REZA NAGHIPOUR
Keyword(s):  
Noetherian Ring ◽  
Cohomological Dimension ◽  
Regular Sequence ◽  
Commutative Noetherian Ring ◽  
Regular Sequences ◽  
Filter Regular Sequence ◽  
Arithmetic Rank

Let I be an ideal of a commutative Noetherian ring R such that ara (I) = t ≥ 2. The purpose of this article is to show that there exists an I-filter regular sequence y1, …, yt for R such that Rad (I) = Rad (y1, …, yt) and cd ((y1, …, yi), R) = i for all 1 ≤ i < t. Also, it is shown that ara (I) ≤ dim R + 1, which is a generalization of a nice result of Kronecker [14]. In addition, some applications are included.

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