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THE NOETHER NUMBER IN INVARIANT THEORY
, 2006
"... Let F be any field. Let G be any reductive linear algebraic group and consider a finite dimensional rational representation V of G. Then the Falgebra F[V] G of polynomial invariants for G acting on V is finitely generated. The Noether Number β(G, V) is the highest degree of an element of a minimal ..."
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Let F be any field. Let G be any reductive linear algebraic group and consider a finite dimensional rational representation V of G. Then the Falgebra F[V] G of polynomial invariants for G acting on V is finitely generated. The Noether Number β(G, V) is the highest degree of an element of a minimal
The Noether numbers for cyclic groups of prime order
, 2005
"... Abstract. The Noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants. We compute the Noether number for an arbitrary representation of a cyclic group of prime order, and as a consequence prove the “2p − ..."
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Abstract. The Noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants. We compute the Noether number for an arbitrary representation of a cyclic group of prime order, and as a consequence prove the “2p
Noether numbers for subrepresentations of cyclic groups of prime order
 BULL. LONDON MATH. SOC
, 2002
"... Let W be a finitedimensional �/pmodule over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W] �/p, is called the Noether number of the representation, and is denoted by β(W). A lower bound for β(W) is derived, and it is shown that i ..."
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Cited by 12 (10 self)
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Let W be a finitedimensional �/pmodule over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W] �/p, is called the Noether number of the representation, and is denoted by β(W). A lower bound for β(W) is derived, and it is shown
BrillNoether theory of curves in toric surfaces
 J. PURE APPL. ALG
, 2014
"... A Laurent polynomial f in two variables naturally describes a projective curve C(f) on a toric surface. We show that if C(f) is a smooth curve of genus at least 7, then C(f) is not BrillNoether general. To accomplish this, we classify all Newton polygons that admit such curves whose divisors all ..."
THE NOETHER EXPONENT AND JACOBI FORMULA
, 1993
"... Abstract. For any polynomial mapping F = (F1,..., Fn) of C n with a finite number of zeros we define the Noether exponent ν(F). We prove the Jacobi formula for all polynomials of degree strictly less than ∑ n i=1 (deg Fi − 1) − ν(F). 1. The Noether exponent If P = P(Z) is a complex polynomial in n ..."
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Abstract. For any polynomial mapping F = (F1,..., Fn) of C n with a finite number of zeros we define the Noether exponent ν(F). We prove the Jacobi formula for all polynomials of degree strictly less than ∑ n i=1 (deg Fi − 1) − ν(F). 1. The Noether exponent If P = P(Z) is a complex polynomial in n
A NoetherLefschetz theorem and applications
 J. Algebraic Geom
, 1995
"... Preliminary version In this paper we generalize the classical NoetherLefschetz Theorem (see [7], [5]) to arbitrary smooth projective threefolds. More specifically, we prove that given any smooth projective threefold X over complex numbers ..."
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Preliminary version In this paper we generalize the classical NoetherLefschetz Theorem (see [7], [5]) to arbitrary smooth projective threefolds. More specifically, we prove that given any smooth projective threefold X over complex numbers
A NOETHER INEQUALITY IN DIMENSION 3
, 2002
"... Abstract. Among complex smooth projective threefolds with ample canonical divisor K, the Noether inequality is of the form K3 ≥ 4 3 pg − δ 3 where pg denotes the geometric genus of the threefold and δ is certain number in {10, 12, 14}. ..."
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Abstract. Among complex smooth projective threefolds with ample canonical divisor K, the Noether inequality is of the form K3 ≥ 4 3 pg − δ 3 where pg denotes the geometric genus of the threefold and δ is certain number in {10, 12, 14}.
Results 1  10
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149