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10,507
Algebraic point set surfaces
 IN PROCEEDINGS SIGGRAPH ’07
, 2007
"... In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar M ..."
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Cited by 80 (8 self)
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In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar
The Canonical Height of an Algebraic Point on an Elliptic Curve
, 2001
"... We use elliptic divisibility sequences to describe a method for estimating the global canonical height of an algebraic point on an elliptic curve. ..."
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Cited by 6 (1 self)
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We use elliptic divisibility sequences to describe a method for estimating the global canonical height of an algebraic point on an elliptic curve.
NéronTate Projection of Algebraic Points
, 2000
"... . Let X be a geometrically irreducible closed subvariety of an abelian variety A over a number field k such that X generates A. Let V be a finitedimensional subspace of A(k)# R, and let # : A(k) # V be the orthogonal projection relative to a NeronTate pairing # , # : A(k) A(k) # R. F ..."
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Cited by 1 (0 self)
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be an abelian variety over k, and let X be a geometrically irreducible closed subvariety of A. Several results describe the location of the rational or algebraic points of X within A. For example, the "MordellLang conjecture" states that if # is a finite rank subgroup of A(k), and if X is not a
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
bounds on the projective heights of algebraic points
 Acta Arith
"... Abstract. If α1,..., αr are algebraic numbers such that r ∑ r∑ N = i=1 αi ̸= i=1 α −1 i for some integer N, then a theorem of Beukers and Zagier [1] gives the best possible lower bound on r∑ log h(αi) i=1 where h denotes the Weil Height. We will extend this result to allow N to be any totally real a ..."
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Cited by 4 (1 self)
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Abstract. If α1,..., αr are algebraic numbers such that r ∑ r∑ N = i=1 αi ̸= i=1 α −1 i for some integer N, then a theorem of Beukers and Zagier [1] gives the best possible lower bound on r∑ log h(αi) i=1 where h denotes the Weil Height. We will extend this result to allow N to be any totally real
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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prediction of some numerical characteristics of the space of algebraic curves in V, especially of genus zero, eventually endowed with a parametrization and marked points. It turned out that
L²Invariants from the Algebraic Point of View
, 2008
"... We give a survey on L²invariants such as L²Betti numbers and L²torsion taking an algebraic point of view. We discuss their basic definitions, properties and applications to problems arising in topology, geometry, group theory and Ktheory. ..."
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Cited by 6 (3 self)
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We give a survey on L²invariants such as L²Betti numbers and L²torsion taking an algebraic point of view. We discuss their basic definitions, properties and applications to problems arising in topology, geometry, group theory and Ktheory.
Dynamic sampling and rendering of algebraic point set surfaces
 COMPUTER GRAPHICS FORUM
, 2008
"... Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving leastsquares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters for curvature ..."
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Cited by 26 (10 self)
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Algebraic Point Set Surfaces (APSS) define a smooth surface from a set of points using local moving leastsquares (MLS) fitting of algebraic spheres. In this paper we first revisit the spherical fitting problem and provide a new, more generic solution that includes intuitive parameters
Ghost systems: A vertex algebra point of view
 Nucl. Phys. B
, 1998
"... Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a oneparameter family of conformal structures. The observation that these structures are related to each other provides a simple way to obtain character formulae for a general twisted module of a g ..."
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Cited by 12 (0 self)
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ghost system. The U(1) symmetry and its subgroups that underly the twisted modules also define an infinite set of invariant vertex subalgebras. Their structure is studied in detail from a Walgebra point of view with particular emphasis on ZNinvariant subalgebras of the fermionic ghost system.
Results 1  10
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10,507