Related papers: A Proof On Arnold-Chekanov Conjecture

The article presents the proof of Casas-Alvero conjecture.

In this paper we prove a generalization of a theorem of Schneider, which gives a criterion for a projective surface over the complex numbers to have an ample cotangent bundle. After reviewing different notions of positivity, we introduce a…

We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Mueller theorem on Ray-Singer torsion and Reidemeister torsion, to the case where the flat vector bundle over a closed manifold carries a nondegenerate symmetric bilinear…

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and…

We prove a part of Shokurov's conjecture on characterization of toric varieties modulo the minimal model program and adjunction conjecture.

We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.

We introduce a ``hybrid'' conjecture which is a common generalisation of the Andr\'e-Oort conjecture and the Andr\'e-Pink-Zannier conjecture and we prove that it is a consequence of the Zilber-Pink conjecture. We also show that our hybrid…

We prove the $p$-curvature conjecture for rank two vector bundles with connection on generic curves, by combining deformation techniques for families of varieties and topological arguments.

We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number…

We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample…

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

In this paper, we prove the non-vanishing conjecture for cotangent bundles on isotrivial elliptic surfaces. Combined with the result by H\"{o}ring and Peternell, it completely solves the question for surfaces with Kodaira dimension at most…

We introduce the concepts of an amazing hypercube decomposition and a double shortcut for it, and use these new ideas to formulate a conjecture implying the Combinatorial Invariance Conjecture of the Kazhdan--Lusztig polynomials for the…

We prove a conjecture of Barraud and Cornea in the monotone setting, refining a result of Chekanov on the Hofer distance between two Hamiltonian isotopic Lagrangian submanifolds.

In this paper we prove that Arnold Surfaces of all real algebraic curves of even degree with non-empty real part are standard (Rokhlin's Conjecture). There is an obvious connection with classification of Arnold Surfaces up to isotopy of S^4…

We describe examples showing the sharpness of Fujita's conjecture on adjoint bundles also in the general type case, and use these examples to formulate related bold conjectures on pluricanonical maps of varieties of general type.

The goal of this paper is to make a surprising connection between several central conjectures in algebraic geometry: the Nonvanishing Conjecture, the Abundance Conjecture, and the Semiampleness Conjecture for nef line bundles on K-trivial…

In this paper we study the problem of density in (1,3] for the Chern ratio of surfaces with ample cotangent bundle. In particular we prove density in (1,2) by constructing a family of complete intersection surfaces in a product of varieties…

Shokurov conjectured that the set of all log canonical thresholds on varieties of bounded dimension satisfies the ascending chain condition. In this paper we prove that the conjecture holds for log canonical thresholds on smooth varieties…