TY - THES
T1 - Rational curves and instantons on the Fano threefold Y_5
Y1 - 2014
A1 - Giangiacomo Sanna
KW - Moduli space of vector bundles
AB - 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-MÃ¼lich 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.
PB - arXiv preprint
UR - http://urania.sissa.it/xmlui/handle/1963/7482
U1 - 7594
U2 - Mathematics
U4 - 1
U5 - MAT/02
ER -