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  • Isomonodromic deformations of logarithmic connections and stable parabolic vector bundles
    Pure Appl. Math. Q. Pub Date : 2020-03-20
    Indranil Biswas; Viktoria Heu; Jacques Hurtubise

    We consider irreducible logarithmic connections $(E, \delta)$ over compact Riemann surfaces $X$ of genus at least two. The underlying vector bundle $E$ inherits a natural parabolic structure over the singular locus of the connection $\delta$; the parabolic structure is given by the residues of $\delta$. We prove that for the universal isomonodromic deformation of the triple $(X, E, \delta)$, the parabolic

    更新日期:2020-03-20
  • Notes on the universal elliptic KZB connection
    Pure Appl. Math. Q. Pub Date : 2020-03-20
    Richard Hain

    In this paper, we give an exposition of the elliptic KZB connection over the universal elliptic curve and use it to compute the limit mixed Hodge structure on the unipotent fundamental group of the first order Tate curve. We also give an explicit algebraic formula for the restriction of the elliptic KZB connection to the moduli space of non-zero abelian differentials on an elliptic curve.

    更新日期:2020-03-20
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