Related papers: $\mathbb{A}^1$-equivalence of zero cycles on surfa…
Recently a simple proof of the generalizations of Hawking's black hole topology theorem and its application to topological black holes for higher dimensional ($n\geq 4$) spacetimes was given \cite{rnew}. By applying the associated new line…
We prove Conjecture F from [VW12] which states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. Moreover, we generalize this conjecture…
In this paper, we prove the Bloch-Beilinson conjecture for certain abelian surfaces over $\mathbb{Q}$, provided that the BSD is known for these abelian surfaces.
In this paper, we propose and study a conjecture that symplectic automorphisms of a $K3$ surface $X$ act trivially on the indecomposable part $\mathrm{CH}^2(X,1)_{\mathrm{ind}}\otimes \mathbb{Q}$ of Bloch's higher Chow group. This is a…
Inspired by the Bloch-Beilinson conjectures, Voisin has formulated a conjecture concerning the behaviour of 0-cycles on self-products of varieties of geometric genus one. This note presents some new examples of surfaces for which Voisin's…
We study Bloch-Ogus theory and the Gersten conjecture for homology theories with duality satisfying certain properties, in particular for \'etale cohomology with finite coefficients coprime to the residue characteristic of the base, for…
We construct a new family of minimal smooth surfaces of general type with K^2=7 and p_g= 0. We show that for a surface in this family, its canonical divisor is ample and its bicanonical morphism is birational. We prove that these surfaces…
We continue the program of classification of normal Q-acyclic surfaces defined over the field of complex numbers, so-called 'Q-homology planes'. Here we show that if a Q-homology plane has negative Kodaira dimension then its smooth locus is…
A compact complex manifold X is said to be rationally cohomologically rigidified if its automorphism group Aut(X) acts faithfully on the cohomology ring H*(X,Q). In this note, we prove that, surfaces of general type with irregularity q>2…
We study zero cycles on rationally connected varieties defined over characteristic zero Laurent fields with algebraically closed residue fields. We show that the degree map induces an isomorphism for rationally connected threefolds defined…
We express the kernel of Griffiths' Abel-Jacobi map by using the inductive limit of Deligne cohomology in the generalized sense (i.e. the absolute Hodge cohomology of A. Beilinson). This generalizes a result of L. Barbieri-Viale and V.…
Let X be a smooth quasi-projective variety over the algebraic closure of the rational number field. We show that the cycle map of the higher Chow group to Deligne cohomology is injective and the higher Hodge cycles are generated by the…
We show that the zero locus of a normal function on a smooth complex algebraic variety S is algebraic provided that the normal function extends to a admissible normal function on a smooth compactification of S with torsion singularity. This…
We study a single-flip dynamics for the monotone surface in (2+1) dimensions obtained from a boxed plane partition. The surface is analyzed as a system of non-intersecting simple paths. When the flips have a non-zero bias we prove that…
We prove that, for translation surfaces whose homology is generated by the periodic orbits, the notions of - finite blocking property - pure periodicity - torus branched covering are equivalent. In particular, we prove this equivalence for…
For a smooth projective variety X, let CH(X) be the Chow ring (with rational coefficients) of algebraic cycles modulo rational equivalence. The conjectures of Bloch and Beilinson predict the existence of a functorial ring filtration of…
In this paper we give a proof of the Bloch-Kato conjecture relating motivic cohomology and etale cohomology. It is a corrected version of the paper with the same title which posted earlier.
This paper is an announcement of the minimal model theory for log surfaces in all characteristics and contains some related results including a simplified proof of the Artin-Keel contraction theorem in the surface case.
It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb{P}^5$, and toric varieties of codimension two. After J.…
We discuss the strong rational connectedness of smooth rationally connected surfaces. We prove in lots of cases, including the smooth locus of a log del Pezzo surface, the rational connectedness indeed implies the strong rational…