You are cordially invited to the seminars organized by the Department of Mathematics.<\/p>\n
Speaker: Neelarnab Raha (Penn State)<\/p>\n
\u201cBrill-Noether theory for vector bundles on surfaces\u201d<\/p>\n
Abstract: The Brill-Noether theory of curves plays a fundamental role in the theory of curves and their moduli and has been intensively studied since the 19th century. In contrast, Brill-Noether theory for higher dimensional varieties is less understood. It is hard to determine when Brill-Noether loci are nonempty, and these loci can be reducible and of larger than the expected dimension.<\/p>\n
Let $E$ be a semistable vector bundle on the projective plane. We give an upper bound $\\beta_{r,\\mu}$ for $h^0(E)$ in terms of the rank $r$ and the slope $\\mu$ of $E$. We show that the bound is achieved precisely when $E$ is a Steiner bundle. We classify those $E$ for which $h^0(E)$ is close to $\\beta_{r,\\mu}$. We determine the nonemptiness, irreducibility and dimension of the Brill-Noether loci with $h^0(E)$ in this range. When they are proper subvarieties, these Brill-Noether loci are irreducible though almost always of larger than the expected dimension. This is joint work with Professors Izzet Coskun and Jack Huizenga.\r\n\r\n We also have a similar bound on the smooth quadric surface, although it is more subtle depending on how balanced the first Chern class is, and what global generation properties the vector bundle possesses.\r\n<\/code><\/pre>\nDate: November 14, Friday
\nTime: 6:00 P.M. (Turkey)
\nPlace: Zoom<\/p>\n
To request the event link, please send a message to turker.ozsari@bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the seminars organized by the Department of Mathematics. Speaker: Neelarnab Raha (Penn State) \u201cBrill-Noether theory for vector bundles on surfaces\u201d Abstract: The Brill-Noether theory of curves plays a fundamental role in the theory of curves and their moduli and has been intensively studied since the [\u2026] <\/p>\n