BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniele Faenzi (Université de Bourgogne) DTSTART:20200916T183000Z DTEND:20200916T200000Z DTSTAMP:20260423T021704Z UID:BRAG/23 DESCRIPTION:Title: St ability of logarithmic tangents\nby Daniele Faenzi (Université de Bou rgogne) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nTo a hypersurface $D$ of projective $N$-space $\\mathbb{P}^N$ one attaches th e \\emph{log\ntangent sheaf} $T_D$ of vector fields of $\\mathbb{P}^N$ tan gent to D. For some highly\nspecial hypersurfaces\, such as\, for instance \, hyperplane arrangements\nassociated to reflection groups and discrimina nts of binary forms\, the\nsheaf $T_D$ splits into line bundles - $D$ is then called \\emph{free}. On the\nother hand\, Dolgachev--Kapranov proved that $T_D$ is stable if $D$ is a\ngeneric arrangement of at least $N+2$ hy perplanes\; also Dimca proved that\n$T_D$ is stable if $D$ has isolated si ngularities with sufficiently small\nTjurina number and $N=3$.\n\nIn this talk we will first show that $T_D$ is stable for a much wider\nclass of hy persurfaces having low-dimensional singularities. In the\nsecond part of t he talk we will prove that $T_D$ is stable if $D$ is the\ndeterminant of $ n\\times n$ matrices.\nIf time allows\, we will discuss the application fr om the equisingular\nHilbert scheme containing $D$ to the moduli space of semistable sheaves\ncontaining $T_D$ and show that it is birational in the case of determinants.\n\nThis is a report on work in progress with S. Mar chesi - soon on the arXiv.\n LOCATION:https://researchseminars.org/talk/BRAG/23/ END:VEVENT END:VCALENDAR