Intersection Numbers of Curves on Hilbert Modular Surfaces and Modular Forms of Nebentypus.
Intersection Numbers of Sections of Elliptic Surfaces.
Intersection theory on Deligne-Mumford compactifications
Intersections sur des courbes modulaires.
Intersection-theoretical computations on
In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].
Introduction aux formes modulaires. Formes modulaires -adiques
Invariance of tautological equations I: conjectures and applications
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to...
Invariant differentials and -functions. Reciprocity law for quadratic fields and elliptic curves over
Invariant Spin Structures on Riemann Surfaces
We investigate the action of the automorphism group of a closed Riemann surface of genus at least two on its set of theta characteristics (or spin structures). We give a characterization of those surfaces admitting a non-trivial automorphism fixing either all of the spin structures or just one. The case of hyperelliptic curves and of the Klein quartic are discussed in detail.
Invariant theory for and the rationality of
Invarianten der degenerierten Fasern in lokalen Familien von Kurven.
Invariants of bi-Lipschitz equivalence of real analytic functions
We construct an invariant of the bi-Lipschitz equivalence of analytic function germs (ℝⁿ,0) → (ℝ,0) that varies continuously in many analytic families. This shows that the bi-Lipschitz equivalence of analytic function germs admits continuous moduli. For a germ f the invariant is given in terms of the leading coefficients of the asymptotic expansions of f along the sets where the size of |x| |grad f(x)| is comparable to the size of |f(x)|.
Invariants of plane algebraic curves via representations of the braid group.
Invariants of singularities of polynomials in two complex variables and the Newton diagrams.
Invariants polaires de courbes planes.
Invariants symétriques et fibrés vectoriels sur les courbes.
Inversion of Abelian Integrals on Small Genus Curves.
Invertibility of Bass-Connell-Wright polynomial maps.
Invertible cohomological field theories and Weil-Petersson volumes
We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....
Irreducibility and monodromy of some families of linear series