A characterization of short curves of a Teichmüller geodesic.
A construction of the Deligne-Mumford orbifold
A differential-geometric approach to deformations of pairs (X, E)
This article gives an exposition of the deformation theory for pairs (X, E), where X is a compact complex manifold and E is a holomorphic vector bundle over X, adapting an analytic viewpoint `a la Kodaira- Spencer. By introducing and exploiting an auxiliary differential operator, we derive the Maurer–Cartan equation and differential graded Lie algebra (DGLA) governing the deformation problem, and express them in terms of differential-geometric notions such as the connection and curvature of E, obtaining...
A foliation of Teichmüller space by twist invariant disks.
A footnote to the Poincaré complete reducibility theorem.
Poincaré's work on the reduction of Abelian integrals contains implicitly an algorithm for the expression of a theta function as a sum of products of theta functions of fewer variables in the presence of reduction. The aim of this paper is to give explicit formulations and reasonably complete proofs of Poincaré's results.
A generalisation of Teichmüller space in the hermitian context
A generalization of Jacobi's derivative formula to dimension two.
A Geometric Algebraicity Property for Moduli Spaces of Compact Kähler Manifolds with h 2, 0 = 1.
A Geometric Study of the Monodromy of Complex Analytic Surfaces.
A Geometry of Kähler Cones.
A Modular Group and Riemann Surfaces of Genus 2.
A natural graded Lie algebra sheaf over Riemann surfaces
A New Compactification of the Siegel Space and Degeneration of Abelian Varieties. I.
A New Compactification of the Siegel Space and Degeneration of Abelian Varieties. II.
A note on geodesics in infinite-dimensional Teichmüller spaces.
A product formula for period integrals.
A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation
The Witten deformation is an analytic method proposed by Witten which, given a Morse function on a smooth compact manifold , allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities...
A pseudo-trigonometry related to Ptolemy's theorem and the hyperbolic geometry of punctured spheres
A hyperbolic geodesic joining two punctures on a Riemann surface has infinite length. To obtain a useful distance-like quantity we define a finite pseudo-length of such a geodesic in terms of the hyperbolic length of its surrounding geodesic loop. There is a well defined angle between two geodesics meeting at a puncture, and our pseudo-trigonometry connects these angles with pseudo-lengths. We state and prove a theorem resembling Ptolemy's classical theorem on cyclic quadrilaterals and three general...
A reduction for asymptotic Teichmüller spaces.
A remark on a deformation theory of Green and Lazarsfeld.