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Rational curves and rational singularities
 Math. Zeitschrift
"... Abstract. We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a C ∗action. For varieties with an isolated singularity, we show that the presence of sufficiently many rational curves outside the singular point strongly affects the character of the sing ..."
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Cited by 11 (3 self)
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Abstract. We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a C ∗action. For varieties with an isolated singularity, we show that the presence of sufficiently many rational curves outside the singular point strongly affects the character
Rational Curves on Complex Manifolds
"... Abstract. We give an overview of the study of rational curves on a complex manifold. Starting from Mori's celebrated theorem on the extremal rays of the cone of curves, we describe some of its applications, and some of the tools used to produce rational curves in Algebraic Geometry and in Kähl ..."
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Abstract. We give an overview of the study of rational curves on a complex manifold. Starting from Mori's celebrated theorem on the extremal rays of the cone of curves, we describe some of its applications, and some of the tools used to produce rational curves in Algebraic Geometry
THE COMPOSITE RATIONAL CURVES AND THEIR SMOOTHNESS
, 2000
"... A model for computing the weights of the control vertices of a rational curve with respect to the continuity constraints is presented. The described method generates for one control polygon a family of curves created from many rational curve segments. The join points of the adjoining curve segments ..."
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A model for computing the weights of the control vertices of a rational curve with respect to the continuity constraints is presented. The described method generates for one control polygon a family of curves created from many rational curve segments. The join points of the adjoining curve segments
Rational curves on K3 surfaces
 J. Alg. Geom
, 1999
"... The classification theory of algebraic surfaces shows there are at most countably many rational curves on a K3 surface. The first question we may ask is whether there are any rational curves at all. The existence of rational curves on a general K3 surface was established in [MM]. A ..."
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Cited by 44 (0 self)
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The classification theory of algebraic surfaces shows there are at most countably many rational curves on a K3 surface. The first question we may ask is whether there are any rational curves at all. The existence of rational curves on a general K3 surface was established in [MM]. A
Generatrices of Rational Curves
, 2001
"... We investigate the oneparametric set G of projective subspaces that is generated by a set of rational curves in projective relation. The main theorem connects the algebraic degree # of G, the number of degenerate subspaces in G and the dimension of the variety of all rational curves that can be use ..."
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Cited by 3 (3 self)
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We investigate the oneparametric set G of projective subspaces that is generated by a set of rational curves in projective relation. The main theorem connects the algebraic degree # of G, the number of degenerate subspaces in G and the dimension of the variety of all rational curves that can
Rational curves and parabolic geometries
, 2007
"... The twistor transform of a parabolic geometry has two steps: lift up to a geometry of higher dimension, and then descend to a geometry of lower dimension. The first step is a functor, but the second requires some compatibility conditions. Local necessary conditions were uncovered by Andreas Čap [12 ..."
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Cited by 3 (3 self)
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[12]. We uncover necessary and sufficient global conditions for complex analytic geometries: rationality of curves defined by certain differential equations. We apply the theorems to second and third order ordinary differential equations to determine whether their solutions are rational curves. We
Rational Curves with Polynomial Parametrization
, 1991
"... : Rational curves and splines are one of the building blocks of computer graphics and geometric modeling. Although a rational curve is more flexible than its polynomial counterpart, many properties of polynomial curves are not applicable to it. For this reason it is very useful to know if a curve pr ..."
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Cited by 6 (1 self)
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: Rational curves and splines are one of the building blocks of computer graphics and geometric modeling. Although a rational curve is more flexible than its polynomial counterpart, many properties of polynomial curves are not applicable to it. For this reason it is very useful to know if a curve
TOPOLOGICAL FIELD THEORY AND RATIONAL CURVES
, 1991
"... We analyze the quantum field theory corresponding to a string propagating on a CalabiYau threefold. This theory naturally leads to the consideration of Witten’s topological nonlinear σmodel and the structure of rational curves on the CalabiYau manifold. We study in detail the case of the world ..."
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Cited by 80 (7 self)
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We analyze the quantum field theory corresponding to a string propagating on a CalabiYau threefold. This theory naturally leads to the consideration of Witten’s topological nonlinear σmodel and the structure of rational curves on the CalabiYau manifold. We study in detail the case of the world
Real Rational curves in Grassmannians
 J. AMER. MATH. SOC
, 1999
"... Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified position with respect to some general fixed figures. For the problem of plane conics tangent to five general conics, the (surprising ..."
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Cited by 13 (5 self)
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, the (surprising) answer is that all 3264 may be real. Similarly, given any problem of enumerating pplanes incident on some general fixed subspaces, there are real fixed subspaces such that each of the (finitely many) incident pplanes are real. We show that the problem of enumerating parameterized rational
Rational Curves on the Space of . . .
, 1998
"... We describe the Hilbert scheme components parametrizing lines and conics on the space of determinantal nets of conics, N. As an application, we use the quantum Lefschetz hyperplane principle to compute the instanton numbers of rational curves on a complete intersection CalabiYau threefold in N. We ..."
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We describe the Hilbert scheme components parametrizing lines and conics on the space of determinantal nets of conics, N. As an application, we use the quantum Lefschetz hyperplane principle to compute the instanton numbers of rational curves on a complete intersection CalabiYau threefold in N. We
Results 1  10
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250,236