BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Simone Marchesi (Universitat de Barcelona) DTSTART:20201118T183000Z DTEND:20201118T200000Z DTSTAMP:20260423T021605Z UID:BRAG/33 DESCRIPTION:Title: Gr oup actions on vector bundles\nby Simone Marchesi (Universitat de Barc elona) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nThe classification of vector bundles which are invariant under the action of a determined group\, has been widely studied.\n\nWe can consider\, for exam ple\, the canonical action of the projective linear group $PGL(n+1)$ on $\ \mathbb{P}^n$ which leads to the definition of homogeneous vector bundle. The choice of specific subgroups has been often determined\, in literature \, restricting our attention to particular families. Recall indeed that An cona and Ottaviani proved that the Steiner bundles on $\\mathbb{P}^n$ that are invariant under an action of $SL(2\,\\mathbb{C})$ are the so called S chwarzenberger bundles. Another example\, moving into the realm of hyperpl ane arrangements\, in which I have been particularly interested lately\, i s given by the reflection arrangements. They are defined as hyperplane arr angements that are invariant under the group generated by their reflection s\, and it is known that their associated sheaf is free (a sum of line bun dles) and therefore homogeneous.\n \nIn a previous work\, studying Nearly -free arrangements\, we proved that their configuration of jumping lines i s extremely special but remarked that it did not characterize this family of arrangements. It turns out that they are characterized by the invarianc e under the action of the subgroup $G_p \\subset \\mathrm{PGL}(3)$ that f ixes the point $p$ in the projective plane. Inspired by this result\, we c lassify vector bundles which are invariant under the action of subgroups t hat fix linear subspaces of the projective plane.\n\nFinally\, we will foc us on the relations between the geometry of the jumping locus and the inva riance under the action of the group. Recall that\, historically\, such qu estion has been studied in order to relate homogeneous bundles with unifor m ones\, i.e. bundles for which the splitting type is constant.\n \nThis i s the result of two collaborations: one with Jean Vallès and one with Ros a Maria Miró-Roig.\n LOCATION:https://researchseminars.org/talk/BRAG/33/ END:VEVENT END:VCALENDAR