Related papers: A characterization of projective spaces from the M…
We establish the minimal model theory for normal pairs along log canonical locus in the complex analytic setting. This is the complex analytic analog of the previous result by the author.
The present paper studies the structure of characteristic varieties of fundamental groups of graph manifolds. As a consequence, a simple proof of Papadima's question is provided on the characterization of algebraic links that have…
This paper proves that the characteristic polynomial is a complete unitary invariant for pairs of projection matrices. Some special cases involving three or more projections are also considered.
It is known that some GIT compactifications associated to moduli spaces of either points in the projective line or cubic surfaces are isomorphic to Baily-Borel compactifications of appropriate ball quotients. In this paper, we show that…
We introduce the new notion of the "quasi-Galois point" in Algebraic geometry, which is a generalization of the Galois point. A point $P$ in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial…
We study extremality properties of covering families of rational curves on projective varieties. Among others, we show that on a normal and Q-factorial projective variety of dimension at most 4, every covering and quasi-unsplit family of…
A couple of complex projective plane curves are said to make a Zariski pair if they have the same degree and the same type of singularities, but their embeddings in the projective plane are topologically different. In this paper, we present…
We give a Hodge theoretic criterion to characterize locally the period domains of certain projective manifolds to be complex balls.
We classify all closed 1-connected manifolds $M$ which look like projective planes, i.e. with integral homology $H_*(M)=Z^3$. Furthermore, we give an explicit construction of these manifolds as Thom spaces of open disk bundles.
The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call such a variety a Mori Dream Space. There…
In this paper, we introduce a new positivity notion for curvature of Riemannian manifolds and obtain characterizations for spherical space forms and the complex projective space $\mathbb{C}\mathbb{P}^n$.
In this paper we prove that a smooth family of canonically polarized manifolds parametrized by a special (in the sense of Campana) quasi-projective variety is isotrivial.
We show that the loop spaces of real projective spaces are topologically approximated by the spaces of rational maps from RP(1) to RP(n). As a byproduct of our constructions we obtain an interpretation of the Kronecker characteristic…
The aim of this paper is to extend the external characterization of I-favorable spaces. This allows us to obtain a characterization of compact I-favorable spaces in terms of quasi k-metrics. We also provide proofs of some author's results…
We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.
The moduli space of jets of certain G-structures (basically those which admit a canonical linear connection) is shown to be isomorphic to the quotient of a natural G-module by G.
This work presents a simple proof that the moduli space of complete integral Gorenstein curves with a prescribed symmetric Weierstrass semigroup becomes a weighted projective space, even for fields of positive characteristic, when the…
This paper is a gentle introduction to the theory of quasi-log varieties by Ambro. We explain the fundamental theorems for the log minimal model program for log canonical pairs. More precisely, we give a proof of the base point free theorem…
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…
In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.