%0 Thesis %D 2014 %T Rational curves and instantons on the Fano threefold Y_5 %A Giangiacomo Sanna %K Moduli space of vector bundles %X This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-Mülich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it. %I arXiv preprint %G en %U http://urania.sissa.it/xmlui/handle/1963/7482 %1 7594 %2 Mathematics %4 1 %# MAT/02 %$ Submitted by gggsanna@sissa.it (gggsanna@sissa.it) on 2014-12-01T10:51:46Z No. of bitstreams: 1 (Official) G. Sanna - Rational curves and instantons on the Fano threefold Y5 copia.pdf: 2005901 bytes, checksum: bd001232412f102490968ba3b21e1c20 (MD5)