Related papers: Semistable reduction for complex analytic spaces

In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).

We discuss vanishing theorems for projective morphisms between complex analytics spaces and some related results. They will play a crucial role in the minimal model theory for projective morphisms of complex analytic spaces. Roughly…

We prove a semistable reduction theorem for principal bundles on curves in almost arbitrary characteristics. For exceptional groups we need some small explicit restrictions on the characteristic.

We establish a version of a semistable reduction theorem over a log point with a non-trivial nilpotent structure. In order to do this we extend the classical desingularization theories to non-reduced schemes with generically principal…

We show that a projective triangulation of a subcomplex of a polyhedral complex can be extended to the whole complex. As a result, we show that the weak semistable reduction result of Abramovich - Karu alg-geom/9707012 can be refined, so…

For a smooth proper scheme over a local field of mixed characteristics which has semistable reduction we define the category of its semistable etale sheaves and under certain hypothesis we prove the appropriate semistable comparison…

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…

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…

In this paper, local monomialization theorems are proven for analytic morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of…

We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a…

We discuss variations of mixed Hodge structure arising from projective morphisms of complex analytic spaces. Then we treat generalizations of Koll\'ar's torsion-free theorem, vanishing theorem, and so on, for reducible complex analytic…

We shall prove an extension of the semipositivity theorem for the case of reducible algebraic fiber spaces.

Let X->B be a morphism of varieties in characteristic zero. Semistable reduction has been proved for dim(B)=1 (Kempf, Knudsen, Mumford, Saint-Donat), dim(X)=dim(B)-1 (de Jong) and dim(X)=dim(B)+2 (Alexeev, Kollar, Shepherd-Barron). In this…

This is a survey article on the recent developments of semipositivity, injectivity, and vanishing theorems for higher-dimensional complex projective varieties.

We study a cut-off function lemma in projective spaces. We believe that this is well-known. We provide the details of the computation for later uses.

We show that certain semistable sheaves on the projective plane with linear Hilbert polynomial are cokernels of semistable morphisms of decomposable sheaves.We exhibit certain locally closed subvarieties of moduli spaces of semistable…

We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.

We restate the semistable reduction theorem from geometric invariant theory in the context of spaces of morphisms on $\mathbb{P}^{n}$. For every complete curve $C$ downstairs, we get a $\mathbb{P}^{n}$-bundle on an abstract curve $D$…

We show a few basic results about moduli spaces of semistable modules over Lie algebroids. The first result shows that such moduli spaces exist for relative projective morphisms of noetherian schemes, removing some earlier constraints. The…

We decompose each moduli space of semistable sheaves on the complex projective plane with support of dimension one and degree four into locally closed subvarieties, each subvariety being the good or geometric quotient of a set of morphisms…