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Browsing by Subject "math.AG"

Now showing items 1-8 of 8

    • Applications to A1-enumerative geometry of the A1-degree 

      Pauli, Sabrina; Wickelgren, Kirsten
      These are lecture notes from the conference Arithmetic Topology at the Pacific Institute of Mathematical Sciences on applications of Morel's A1-degree to questions in enumerative geometry. Additionally, we give ...

    • Compactly supported $\mathbb{A}^{1}$-Euler characteristic and the Hochschild complex 

      Arcila-Maya, Niny; Bethea, Candace; Opie, Morgan; Wickelgren, Kirsten; Zakharevich, Inna (2020-03-20)
      We show the $\mathbb{A}^{1}$-Euler characteristic of a smooth, projective scheme over a characteristic $0$ field is represented by its Hochschild complex together with a canonical bilinear form, and give an exposition of ...

    • Hodge theory of the Goldman bracket 

      Hain, Richard (Geometry and Topology, 2020-01-01)
      In this paper we show that, after completion in the I-adic topology, the Goldman bracket on the space spanned by homotopy classes of loops on a smooth, complex algebraic curve is a morphism of mixed Hodge structure. ...

    • Hodge Theory of the Turaev Cobracket and the Kashiwara--Vergne Problem 

      Hain, Richard (Journal of the European Mathematical Society, 2021-01-01)
      In this paper we show that, after completing in the $I$-adic topology, the Turaev cobracket on the vector space freely generated by the closed geodesics on a smooth, complex algebraic curve $X$ with an algebraic framing ...

    • Mirror Symmetry and Discriminants 

      Aspinwall, Paul S; Plesser, M Ronen; Wang, Kangkang
      We analyze the locus, together with multiplicities, of "bad" conformal field theories in the compactified moduli space of N=(2,2) superconformal field theories in the context of the generalization of the Batyrev ...

    • Notes on Projective, Contact, and Null Curves 

      Bryant, Robert
      These are notes on some algebraic geometry of complex projective curves, together with an application to studying the contact curves in CP^3 and the null curves in the complex quadric Q^3 in CP^4, related by the well-known ...

    • Notes on the Universal Elliptic KZB Equation 

      Hain, R (Pure and Applied Mathematics Quarterly, 2020-01-30)
      The universal elliptic KZB equation is the integrable connection on the pro-vector bundle over M_{1,2} whose fiber over the point corresponding to the elliptic curve E and a non-zero point x of E is the unipotent completion ...

    • Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces 

      Bryant, RL (2001-03-05)
      I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid ...