Related papers: The stable and augmented base locus under finite m…
In the setting of relative topos theory, we show that the pullback of a relative presheaf topos on an arbitrary fibration is the relative presheaf topos on its inverse image. To this end, we develop and exploit a notion of extension with…
This note contains some results related to the definitions of toroidal embeddings and toroidal morphisms over non-closed fields of characteristic zero.
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…
We explore very stable and wobbly bundles, twisted in a particular sense by a line bundle, over complex algebraic curves of genus $1$. We verify that twisted stable bundles on an elliptic curve are not very stable for any positive twist. We…
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 my PhD Thesis, part of it has published in Acta Mathematica Sinica. In this paper, a class of morphisms which have a kind of singularity weaker than normal crossing is considered. We construct the obstruction such that the so-called…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
Let $A$ be a commutative augmented ring and $I$ be its augmentation ideal. This paper shows that the sequence $\{I^n/I^{n+1}\}$ becomes stationary up to isomorphism. The result yields stability in the associated graded ring of $A$ along…
For $\mathrm{O}(\mathrm{q},k)$, the orthogonal group over a field $k$ of characteristic 2 with respect to a quadratic form $\mathrm{q}$, we discuss the isomorphism classes of fixed points of involutions. When the quadratic space is either…
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…
In this article we investigate the regularity properties of linear degenerations of flag varieties. We classify the linear degenerations of (partial) flag varieties that are smooth. Furthermore, we study the singular locus of irreducible…
We study the geometry of the morphism between moduli spaces of hypersurfaces in $\mathbb P^{n-1}$ that sends a smooth hypersurface of degree $d+1$ to its associated hypersurface of degree $n(d-1)$. As a result, we obtain a compactification…
We study the spaces of polynomials stratified into the sets of polynomial with fixed number of roots inside certain semialgebraic region $\Omega$, on its border, and at the complement to its closure. Presented approach is a generalisation,…
We establish sharp quantitative stability estimates near finite sums of ground states. The results depend on the dimension and the order of nonlinearity.
The difference between the Faltings height of an abelian variety $A$ defined over a number field $k$ and its stable height is measured by the so-called base change conductor. In this paper, we give a uniform bound of the base change…
We present a general regularization procedure for piecewise smooth vector fields whose discontinuity locus is a variety of normal crossings type. We show that such regularization can be smoothed through a finite sequence of blowings-up,…
A Laurent polynomial in two variables is tempered if its edge polynomials are cyclotomic. Variation of coefficients leads to a family of smooth complete genus $g$ curves carrying a canonical algebraic $K_2$-class over a $g$-dimensional base…
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…
An algebraic proof is presented for the finite strong standard completeness of involutive uninorm logic with fixed point. The result may provide a first step towards settling the open standard completeness problem for involutive uninorm…
A phase-separation front will leave in its wake a phase-separated morphology that differs markedly from homogeneous phase-separation morphologies. For a purely diffusive system such a front, moving with constant velocity, will generate very…