相关论文: The theorem of Mather on generic projections for s…

We prove that the Tate conjecture for divisors is ''generically true'' for mod p reductions of complex projective varieties with $h^{2, 0} = 1$, under a mild assumption on moduli. By refining this general result, we establish a new case of…

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we…

We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.

An important result in real algebraic geometry is the projection theorem: every projection of a semialgebraic set is again semialgebraic. This theorem and some of its conclusions lie at the basis of many other results, for example the…

We show that two smooth projective curves C_1 and C_2 of genus g which have isomorphic symmetric products are isomorphic unless g=2. This extends a theorem of Martens.

We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of…

In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.

In earlier papers it was shown that the generic tropical variety of an ideal can contain information on algebraic invariants as for example the depth in a direct way. The existence of generic tropical varieties has so far been proved in the…

We prove the invariance of plurigenera under smooth projective deformations in full generality. The proof is done by several estimates of singular hermitian metrics in terms of $L^{2}$-extension theorem of holomorphic sections.

We extend the holomorphic analytic torsion classes of Bismut and K\"ohler to arbitrary projective morphisms between smooth algebraic complex varieties. To this end, we propose an axiomatic definition and give a classification of the…

In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.

We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…

We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.

We study the GKM theory for a equivariant stratified space having orbifold structures in tis successive quotients. Then, we introduce the notion of an \emph{almost simple polytope}, as well as a \emph{divisive toric variety} generalizing…

We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

In this paper we study the question asked by Caucher Birkar about injectivity theorem on cohomologies of generalised pairs. By applying techniques from complex analytic geometry, we show that the injectivity theorem holds for generalised…

This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal…

We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…

In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…