A conic bundle degenerating on the Kummer surface |
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Authors: | Michele Bolognesi |
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Institution: | (1) Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy |
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Abstract: | Let C be a genus 2 curve and the moduli space of semi-stable rank 2 vector bundles on C with trivial determinant. In Bolognesi (Adv Geom 7(1):113–144, 2007) we described the parameter space of non stable extension
classes of the canonical sheaf ω of C by ω−1. In this paper, we study the classifying rational map that sends an extension class to the corresponding rank two vector bundle. Moreover, we prove that, if we blow up along a certain cubic surface S and at the point p corresponding to the bundle , then the induced morphism defines a conic bundle that degenerates on the blow up (at p) of the Kummer surface naturally contained in . Furthermore we construct the -bundle that contains the conic bundle and we discuss the stability and deformations of one of its components. |
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