Results 1  10
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902
Reduction number of links of irreducible varieties
 J. Pure and Applied Algebra
, 1997
"... The reductions of an ideal I give a natural pathway to the properties of I, with the advantage of having fewer generators. In this paper we primarily focus on a conjecture about the reduction exponent of links of a broad class of primary ideals. The existence of an algebra structure on the Koszul an ..."
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Cited by 8 (3 self)
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The reductions of an ideal I give a natural pathway to the properties of I, with the advantage of having fewer generators. In this paper we primarily focus on a conjecture about the reduction exponent of links of a broad class of primary ideals. The existence of an algebra structure on the Koszul and Eagon–Northcott resolutions is the main tool for detailing the known cases of the conjecture. In the last section we relate the conjecture to a formula involving the length of the first Koszul homology modules of these ideals.
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 506 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
Irreducible components of varieties of modules
 J. REINE ANGEW. MATH
, 2002
"... We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are quite different, being based on deformation theory. ..."
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Cited by 45 (7 self)
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We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are quite different, being based on deformation theory.
Irreducible components of characteristic varieties
, 2001
"... We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial differential equations de ned froma suitable ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety defined fromthe order ..."
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Cited by 9 (1 self)
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We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial differential equations de ned froma suitable ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety defined fromthe order
ON THE IRREDUCIBLE COMPONENTS OF CHARACTERISTIC VARIETIES
, 2007
"... Abstract. This is a quick survey on the characteristic varieties associated to rank one local systems on a smooth, irreducible, quasiprojective complex variety M. A key new result is Proposition 1.8, giving additional information on the constructible sheaf F = R 0 f∗(L), where L is a rank one local ..."
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Abstract. This is a quick survey on the characteristic varieties associated to rank one local systems on a smooth, irreducible, quasiprojective complex variety M. A key new result is Proposition 1.8, giving additional information on the constructible sheaf F = R 0 f∗(L), where L is a rank one
Nonarchimedean amoebas and tropical varieties
, 2004
"... We study the nonarchimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For hypersurfaces this set is also the tropical variety of the defining polynomial. Using nonarchimedean analysis a ..."
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Cited by 144 (0 self)
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and a recent result of Conrad we prove that the amoeba of an irreducible variety is connected. We introduce the notion of an adelic amoeba for varieties over global fields, and establish a form of the localglobal principle for them. This principle is used to explain the calculation of the nonexpansive
On irreducible components of a Weierstrasstype variety
 Ann. Polonici Mat
, 1997
"... Abstract. We give a characterization of the irreducible components of a Weierstrasstype (W type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component ..."
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Cited by 1 (0 self)
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Abstract. We give a characterization of the irreducible components of a Weierstrasstype (W type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a
On the irreducibility of commuting varieties of nilpotent matrices
"... Given an n × n nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the n × n nilpotent matrices over K which commute with it. Then we give a proof of the irreducibility of the variety of all the pairs (A, B) of n × n nilpotent matrices over K such that [ ..."
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Cited by 22 (2 self)
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Given an n × n nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the n × n nilpotent matrices over K which commute with it. Then we give a proof of the irreducibility of the variety of all the pairs (A, B) of n × n nilpotent matrices over K
A new sixdimensional irreducible symplectic variety
 J. Alg. Geom
"... 1. Introduction. There are three types of “building blocks ” in the Bogomolov decomposition [B, Th.2] of compact Kählerian manifolds with torsion c1, namely complex tori, CalabiYau varieties, and irreducible symplectic manifolds. We are interested in the last type, i.e. simplyconnected compact Käh ..."
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Cited by 58 (2 self)
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1. Introduction. There are three types of “building blocks ” in the Bogomolov decomposition [B, Th.2] of compact Kählerian manifolds with torsion c1, namely complex tori, CalabiYau varieties, and irreducible symplectic manifolds. We are interested in the last type, i.e. simplyconnected compact
Results 1  10
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902