Related papers: A generalization of twistor lines for complex tori
This article uses basic homological methods for evaluating examples of compactly supported cohomology groups of line bundles over projective curve.
We introduce a new notion of generalized log twisted curves, which are marked nodal curves with additional data at the marked points. In the case when the markings are distinct this notion agrees with the notion of twisted curve introduced…
Normal forms of almost complex structures in a neighborhood of pseudoholomorphic curve are considered. We define normal bundles of such curves and study the properties of linear bundle almost complex structures. We describe 1-jet of the…
Given a smooth and projective curve C and a smooth and projective toric variety X, we first describe a compactification of the space of morphisms from C to X representing a fixed homology class, and after we study the intersection theory on…
This is a review article discussing the de Rham cohomology of period domains of Hodge structures. We explain it as the de Rham cohomology of differentiable stacks as of a moduli space. We also discuss the cohomology of the partial toroidal…
We generalize a compactification technique due to C. Simpson in the context of $\mathbb{G}_m$-actions over the ground field of complex numbers, to the case of a universally Japanese base ring. We complement this generalized compactification…
In this paper, we construct a compactification of the space of Bridgeland stability conditions on a smooth projective curve, as an analogue of Thurston compactifications in Teichm\"uller theory. In the case of elliptic curves, we compare…
We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all…
We propose an explicit relation between the cohomology of compactified and noncompactified moduli spaces of algebraic curves with punctures. This relationship generalizes one between commutative algebras and Lie algebras proposed by Lazard,…
We introduce and study a new class of compactified Jacobians for nodal curves, that we call compactified Jacobians of vine type, or simply V-compactified Jacobians. This class is strictly larger than the class of classical compactified…
The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a…
We prove autoduality for curves of compact type and, more generally, treelike curves with planar singularities. More precisely, we produce an isomorphism between the generalized Jacobian of such a curve and the connected component of the…
We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP^2. Here, line means a smooth rational curve whose normal bundle is O(1)^2 and the reality implies the invariance under an anti-holomorphic…
We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that…
Tractrices of planar curves, in particular, a family of tractrices of a circle, are considered. Some new observations (including arc-length parametrization, Chezaro equation) and corrected reference informations are provided. The article is…
We report on a new approach, as well as some related experiments, to construct families of K3 surfaces having real or complex multiplication. The approach is based on an explicit description of the transcendental part of the cohomology in a…
The prototypical examples of tropical compactifications are compactifications of complements of hyperplane arrangements, which posses a number of remarkable properties not satisfied by more general tropical compactifications of closed…
We study non-commutative degenerations of elliptic curves over local fields. The corresponding objects are close relatives of non-commutative tori of Connes and Rieffel.
We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomology of period domains and the complex structure on symmetric…
This paper describes the construction of a canonical compactification of the space of trajectories and of the unstable/stable sets of a generic gradient like vector field on a closed manifold as well as a canonical structure of a smooth…