MENU

You are here

Rational curves and instantons on the Fano threefold Y_5

TitleRational curves and instantons on the Fano threefold Y_5
Publication TypeThesis
Year of Publication2014
AuthorsSanna, G
UniversityarXiv preprint
KeywordsModuli space of vector bundles
Abstract

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.

URLhttp://urania.sissa.it/xmlui/handle/1963/7482
Custom 1

7594

Custom 2

Mathematics

Custom 4

1

Custom 5

MAT/02

Custom 6

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)

Sign in