Related papers: Relation Between Hyperelliptic Integrals
The classical approach to visualizing a flow, in terms of its streamlines, motivates a topological/soft-analytic argument for constrained variational equations. In its full generality, that argument provides an explicit formula for…
We construct nontrivial L-equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L-equivalence for curves (necessarily over…
In this note a proof is given for global existence and uniqueness of minimal surfaces of Lorentzian type from a cylinder into globally hyperbolic Lorentzian manifolds for given initial values up to the first derivatives.
Let $X$ be a quadratic vector field with a center whose generic orbits are algebraic curves of genus one. To each $X$ we associate an elliptic surface (a smooth complex compact surface which is a genus one fibration). We give the list of…
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…
We construct a general class of correspondences on hyperelliptic Riemann surfaces of arbitrary genus that combine finitely many Fuchsian genus zero orbifold groups and Blaschke products. As an intermediate step, we first construct analytic…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
We show that any pseudo-effective divisor on a normal surface decomposes uniquely into its "integral positive" part and "integral negative" part, which is an integral analog of Zariski decompositions. By using this decomposition, we give…
This expository survey describes how holomorphic quadratic differentials arise in several aspects of Teichm\"uller theory, highlighting their relation with various geometric structures on surfaces. The final section summarizes results for…
A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular we prove that, under some natural assumption, any…
We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically…
A stream of new theta relations is obtained. They follow from the general Thomae formula, which is a new result giving expressions for theta derivatives (the zero values of the lowest non-vanishing derivatives of theta functions with…
We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.
Using the path lattice cohomology we provide a conceptual topological characterization of the geometric genus for certain complex normal surface singularities with rational homology sphere links, which is uniformly valid for all…
This paper is devoted to the horizontal (``characteristic'') cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov…
We give a full exceptional collection in the triangulated category of singularities in the sense of Orlov for a hypersurface singularity of Fermat type, and discuss its relation with homological mirror symmetry for simple elliptic…
In this paper, we consider Hessian equations with its structure as a combination of elementary symmetric functions on closed K\"ahler manifolds. We provide a sufficient and necessary condition for the solvability of these equations, which…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We present multiresidue formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantum Knizhnik--Zamolodchikov equation at generic values of the quantum parameter q. These allow for…
For a holomorphic function on a complex manifold, we show that the vanishing cohomology of lower degree at a point is determined by that for the points near it, using the perversity of the vanishing cycle complex. We calculate it explicitly…