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Asymptotic behaviour of rational curves
Asymptotic behaviour rational curves Algebraic Geometry
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2011/9/15
Abstract: We investigate the asympotic behaviour of the moduli space of morphisms from the rational curve to a given variety when the degree becomes large. One of the crucial tools is the homogeneous ...
On a conjecture of Oguiso about rational curves on Calabi-Yau threefolds
Calabi-Yau threefold, rational curve, nef cone, rational points of cubic forms, Kobayashi's conjecture
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2011/9/13
Abstract: Let X be a Calabi-Yau threefold. We show that if there exists on X a non-zero nef non-ample divisor then X contains a rational curve, provided its second Betti number is greater than 4.
Rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3
Rational curves supersingular K3 surface Artin invariant 1 Algebraic Geometry
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2011/8/30
Abstract: We show the existence of 112 non-singular rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3 by several ways. Using these rational curves, we have a $...