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277,770
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 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 46 (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 2 (2 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
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 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 7 (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
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
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 81 (6 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
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
Rational curves and parabolic geometries
, 2008
"... The twistor transform of a parabolic geometry has two steps: lift up to a geometry of higher dimension, and then drop 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 [9]. I ..."
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]. I prove necessary and sufficient global conditions for complex parabolic geometries: rationality of curves defined by certain ordinary differential equations. I harness Mori’s bend–andbreak to show that any parabolic geometry on any closed Kähler manifold containing a rational curve is inherited
ON THE EXISTENCE OF ARCS IN RATIONAL CURVES
"... A rationat continuum is a compact connected metric space which has a basis of open sets with countable boundaries. Rational curves which contain no arcs have interested topolo gists for a long time. In 1912, Z. Janiszewski (see [2]) con structed an arclike rational curve which contains no arcs. In 1 ..."
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A rationat continuum is a compact connected metric space which has a basis of open sets with countable boundaries. Rational curves which contain no arcs have interested topolo gists for a long time. In 1912, Z. Janiszewski (see [2]) con structed an arclike rational curve which contains no arcs
Results 1  10
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277,770