相关论文: Integrable Top Equations associated with Projectiv…
An explicit construction is presented of homotopy-invariant iterated integrals on a Riemann surface of arbitrary genus in terms of a flat connection valued in a freely generated Lie algebra. The integration kernels consist of modular…
In this paper we compute certain two-point integrals over a moduli space of stable maps into projective space. Computation of one-point analogues of these integrals constitutes a proof of mirror symmetry for genus-zero one-point…
In our previous work, we provided an algebraic proof of the Zinger's comparison formula between genus one Gromov-Witten invariants and reduced invariants when the target space is a complete intersection of dimension two or three in a…
We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical…
In this first of a series of three papers we outline an approach to classifying 4d $\mathcal{N}{=}2$ superconformal field theories at rank 2. The classification of allowed scale invariant $\mathcal{N}=2$ Coulomb branch geometries of…
We describe the results that have so far been obtained in the classification problem for integrable (2+1)-dimensional systems of hydrodynamic type. The systems of Gibbons--Tsarev type are the most fundamental here. A whole class of…
We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…
We are solving the classical Riemann-Hilbert problem of rank N>1 on the extended complex plane punctured in 2m+2 points, for NxN quasi-permutation monodromy matrices. Following Korotkin we solve the Riemann-Hilbert problem in terms of the…
A four-dimensional integrable rigid-body system is considered and it is shown that it represents two twisted three-dimensional Lagrange tops. A polynomial Lax representation, which doesn't fit neither in Dubrovin's nor in Adler - van…
We prove the conjecture that two projective symplectic resolutions for a symplectic variety $W$ are related by Mukai's elementary transformations over $W$ in codimension 2 in the following cases: (i). nilpotent orbit closures in a classical…
We define the notion of log-Riemann surfaces and Caratheodory convergence of log-Riemann surfaces. We prove a convergence theorem for uniformizations of simply connected log-Riemann surfaces converging in the Caratheodory topology. We…
We give an algorithm for finding conformal mappings onto the upper half-plane and conformal modules of some types of polygons. The polygons are obtained by stretching along the real axis polyominoes i.e., polygons which are connected unions…
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…
The projective shape of a configuration of k points or "landmarks" in RP(d) consists of the information that is invariant under projective transformations and hence is reconstructable from uncalibrated camera views. Mathematically, the…
We introduce the class of transparent embeddings for a point-line geometry $\Gamma = ({\mathcal P},{\mathcal L})$ as the class of full projective embeddings $\varepsilon$ of $\Gamma$ such that the preimage of any projective line fully…
It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions. Analogies with the finite-dimensional…
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution…
N=(2,2), d=2 supersymmetric non-linear sigma-models provide a physical realization of Hitchin's and Gualtieri's generalized Kaehler geometry. A large subclass of such models are comprised by WZW-models on even-dimensional reductive group…
In this paper, we study supersymmetric or bi-superhamiltonian Euler equations related to the generalized Neveu-Schwarz algebra. As an application, we obtain several supersymmetric or bi-superhamiltonian generalizations of some well-known…
We prove that for a system of indeterminates (X_a) indiced by the P^2(2), the projective plane over F_2, there exists a 3-3 correspondance compatible with the incidence structures of P^2(2), such that (X_a) is one of the orbits of it. We…