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Moduli of roots of line bundles on curves
We treat the problem of completing the moduli space for roots of line bundles on curves. Special attention is devoted to higher spin curves within the universal Picard scheme. Two new differentExpand
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Contractible classes in toric varieties
Let X be a smooth, complete toric variety. Let A1(X) be the group of algebraic 1-cycles on X modulo numerical equivalence and N1(X) = A1(X)⊗ZQ . Consider inN1(X) the coneNE(X) generated by classes ofExpand
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Sur une conjecture de Mukai
RésuméGénéralisant une question de Mukai, nous conjecturons qu’une variété de Fano X de nombre de Picard ρX et de pseudo-indice ιX vérifie $ρX (ιX - 1) ≤ dim(X). Nous démontrons cette conjectureExpand
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Locally Unsplit Families of Rational Curves of Large Anticanonical Degree on Fano Manifolds
In this paper we address Fano manifolds X with a locally unsplit dominating family of rational curves of anticanonical degree equal to the dimension of X. We first observe that their Picard number isExpand
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Centrally symmetric generators in toric Fano varieties
Abstract.We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has ``many'' pairs of centrally symmetric vertices.
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Moduli of Prym curves
Here we focus on the compactification of the moduli space of curves of genus g together with an unramified double cover, constructed by Arnaud Beauville in order to compactify the Prym mapping. WeExpand
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Combinatorial Properties of Stable Spin Curves
Abstract The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph-theoretic framework is not just aExpand
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Quasi-elementary contractions of Fano manifolds
Abstract Let X be a smooth complex Fano variety. We study ‘quasi-elementary’ contractions of fiber type of X, which are a natural generalization of elementary contractions of fiber type. If f:X→Y isExpand
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On the Picard number of divisors in Fano manifolds
Let X be a complex Fano manifold of arbitrary dimension, and D a prime divisor in X. We consider the image H of N_1(D) in N_1(X) under the natural push-forward of 1-cycles. We show that theExpand
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Projective Q-factorial toric varieties covered by lines
We give a structural theorem for ℚ-factorial toric varieties covered by lines in ℙN, and compute their dual defect. This yields a characterization of defective ℚ-factorial toric varieties in ℙN. TheExpand
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