Related papers: Meromorphic connections on the projective line wit…
We study a number of local and global classification problems in generalized complex geometry. In the first topic, we characterize the local structure of generalized complex manifolds by proving that a generalized complex structure near a…
We show that $J-$ stability is open and dense in natural families of meromorphic maps of one complex variable with a finite number of singular values, and even more generally, to finite type maps. This extends the results of…
We prove that a meromorphic map defined on the complement of a compact subset of a three-dimensional Stein manifold M and with values in a compact complex three-fold X extends to the complement of a finite set of points. If X is simply…
We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves…
We describe an application of tropical moduli spaces to complex dynamics. A post-critically finite branched covering $\varphi$ of $S^2$ induces a pullback map on the Teichm\"uller space of complex structures of $S^2$; this descends to an…
Let $R$ be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules $(M,N)$ over $R$ we study applications of rigidity of $\Tor^R(M,N)$, based on ideas by Huneke, Wiegand and Jorgensen. We then focus…
In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective…
A local model of the dielectric response of a metal predicts that singular surfaces, such as sharp-edged structures, have a continuous absorption spectrum and extreme concentration of energy at the singularity. Here we show that nonlocality…
The purpose of this is the study of certain coherent sheaves of meromorphic forms on reduced complex space and particularly their behavior with respect to pull back and higher direct image.
Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases of these spaces arise as moduli spaces of semistable…
In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational singularities and prove basic properties of such objects. Natural examples of singular…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
This paper review one construction of Frobenius manifolds (and slightly weaker structures). It splits it into several steps and discusses the freedom and the constraints in these steps. The steps pass through holomorphic bundles with…
We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…
We describe the local and global structure of the fixed locus for the action of a rational function on the Berkovich projective line over a complete nontrivially-valued algebraically closed nonarchimedean field. This includes a bound for…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…
We survey some recent results concerning the behaviour of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.
Let G be a connected reductive group and X be a smooth curve over an algebraically closed field of characteristic zero. We show that every meromorphic G-connection on X admits a possibly degenerate oper structure; in particular, every…
We study rationality properties of geodesic cycle integrals of meromorphic modular forms associated to positive definite binary quadratic forms. In particular, we obtain finite rational formulas for the cycle integrals of suitable linear…