Related papers: A generalization of twistor lines for complex tori
A curve, that is, a connected, reduced, projective scheme of dimension 1 over an algebraically closed field, admits two types of compactifications of its (generalized) Jacobian: the moduli schemes of P-quasistable torsion-free, rank-1…
The type of a complex projective plane curve has been recently introduced by T. Abe, P. Pokora and the first author. In the same paper they have studied the type two curves. In this paper we study plane curves of type three, with special…
Our paper develops a theory of Poisson slices and a uniform approach to their partial compactifications. The theory in question is loosely comparable to that of symplectic cross-sections in real symplectic geometry.
We use orientations on stable graphs to express the combinatorial structure of the compactified universal Jacobians in degrees g-1 and g over the moduli space of stable curves, \Mgb, and construct for them graded stratifications compatible…
This is a short report on our new vanishing theorems for projective morphisms between complex analytic spaces. We established a complex analytic generalization of Koll\'ar's torsion-freeness and vanishing theorem for analytic simple normal…
The goal of the present paper is to construct a smooth compactification of the moduli superstack classifying pointed $\mathcal{N} =1$ SUSY (= $\text{SUSY}_1$) curves. This construction is based on the Abramovich-Jarvis-Chiodo…
In this paper we prove a conjecture of Griffiths about vanishing of the zeroth cohomology groups of locally homogeneous vector bundles on compact quotients of non-classical period domains, and construct a new $G_\R$-invariant complex…
This is a survey of some results on the structure and classification of normal analytic compactifications of C^2. Mirroring the existing literature, we especially emphasize the compactifications for which the curve at infinity is…
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs(digraphs). We obtain a new notion of the…
We give new examples of algebraic integral cohomology classes on smooth projective complex varieties that are not integral linear combinations of classes of smooth subvarieties. Some of our examples have dimension 6, the lowest possible.…
Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. When seen as a function of the frequency this invariant collection of tori is called…
In this paper we study the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relation between the topology and certain torsion classes in the Picard group of degree zero of the…
This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…
This article treats compactifications of the space of generalized spin curves. Generalized spin curves, or $r$-spin curves, are pairs $(X,L)$ with $X$ a smooth curve and $L$ a line bundle whose r-th tensor power is isomorphic to the…
In this paper we will study the moduli spaces of log Hodge structures introduced by Kato-Usui. This moduli space is a partial compactification of a discrete quotient of a period domain. We treat the following 2 cases: (A) the case where the…
We study toroidal compactifications of string theories which include compactification of a timelike coordinate. Some new features in the theory of toroidal compactifications arise. Most notably, Narain moduli space does not exist as a…
In this paper, we introduce a new class of curves \alpha called a f-rectifying curves, which its f-position vector defined by {\alpha}_{f}(s)=\int f(s)T(s)ds always lie in the rectifying plane of \alpha, where f is an integrable function…
We survey our works on the locally analytic vectors of completed cohomology of modular curves.
In the classical theory of toric manifolds polytopes appear in two guises -- as Newton polytopes of line bundles on the complex, and as moment polytopes on the symplectic side, the link between the two being established by the…
We use the theory of logarithmic line bundles to construct compactifications of spaces of roots of a line bundle on a family of curves, generalising work of a number of authors. This runs via a study of the torsion in the tropical and…