2011/10/27 by Mboyo Esole, James Fullwood, Esole, Mboyo +3
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.1110.6177
openalex publication_date 2011/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A D5 elliptic fibration is a fibration whose generic fiber is modeled by the\ncomplete intersection of two quadric surfaces in P3. They provide simple\nexamples of elliptic fibrations admitting a rich spectrum of singular fibers\n(not all on the list of Kodaira) without introducing singularities in the total\nspace of the fibration and therefore avoiding a discussion of their\nresolutions. We study systematically the fiber geometry of such fibrations\nusing Segre symbols and compute several topological invariants.\n We present for the first time Sen's (orientifold) limits for D5 elliptic\nfibrations. These orientifolds limit describe different weak coupling limits of\nF-theory to type IIB string theory giving a system of three brane-image-brane\npairs in presence of a Z2 orientifold. The orientifold theory is\nmathematically described by the double cover the base of the elliptic\nfibration. Such orientifold theories are characterized by a transition from a\nsemi-stable singular fiber to an unstable one. In this paper, we describe the\nfirst example of a weak coupling limit in F-theory characterized by a\ntransition to a non-Kodaira (and non-ADE) fiber. Inspired by string dualities,\nwe obtain non-trivial topological relations connecting the elliptic fibration\nand the different loci that appear in its weak coupling limit. Mathematically,\nthese are surprising relations relating the total Chern class of the D5\nelliptic fibration and those of different loci that naturally appear in the\nweak coupling limit. We work in arbitrary dimension and our results don't\nassume the Calabi-Yau condition.\n