다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

Théorie de Hodge et géomětrie algěbrique complexe

/pdf/classical-algebraic-geometry-3wzv0dreho.pdf

Classical Algebraic Geometry

Mumford's theorem is usually read as indicating that for a general variety, the Chow groups are \"very large\" in codimension > 1. But another way of paraphrasing Mumford's theorem is that varieties with \"small\" Chow groups have very special properties. This last idea is systematically explored by Bloch and Srinivas [B-S]. Observing that A ir \" X is finite dimensional if A 0 (X ,) has support on a curve (for a universal

/pdf/algebraic-varieties-with-small-chow-groups-44bbu95nr0.pdf

Algebraic varieties with small Chow groups

This note is about certain locally complete families of Calabi–Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cycle class map on the Chow ring of powers of these varieties admits a section, and that these varieties admit a multiplicative self-dual Chow–Kunneth decomposition. As a consequence of both results, we prove that the subring of the Chow ring generated by divisors, Chern classes, and intersections of two cycles of positive codimension injects into cohomology via the cycle class map. We also prove that the small diagonal of Schreieder surfaces admits a decomposition similar to that of K3 surfaces. As a by-product of our main result, we verify a conjecture of Voisin concerning zero-cycles on the self-product of Cynk–Hulek Calabi–Yau varieties, and in the odd-dimensional case we verify a conjecture of Voevodsky concerning smash-equivalence. Finally, in positive characteristic, we show that the supersingular Cynk–Hulek Calabi–Yau varieties provide examples of Calabi–Yau varieties with “degenerate” motive.

On the Chow Ring of Cynk–Hulek Calabi–Yau Varieties and Schreieder Varieties

https://hal.archives-ouvertes.fr/hal-01653196/document

The generalized Franchetta conjecture for some hyper-Kähler varieties

Let X be a smooth cubic hypersurface, and let F be the Fano variety of lines on X. We establish a relation between the Chow motives of X and F. This relation implies in particular that if X has finite-dimensional motive (in the sense of Kimura), then F also has finite-dimensional motive. This proves finite-dimensionality for motives of Fano varieties of cubics of dimension 3 and 5, and of certain cubics in other dimensions.

A remark on the motive of the Fano variety of lines of a cubic

Given a smooth projective variety, a Chow–Kunneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kahler varieties admit a multiplicative Chow–Kunneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kahler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Kunneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Kuchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow–Kunneth decomposition, by establishing this for two families of Todorov surfaces.

/pdf/multiplicative-chow-kunneth-decompositions-and-varieties-of-jw0w226dq8.pdf

Robert Laterveer

Papers

Algebraic varieties with small Chow groups

On the Chow Ring of Cynk–Hulek Calabi–Yau Varieties and Schreieder Varieties

The generalized Franchetta conjecture for some hyper-Kähler varieties

A remark on the motive of the Fano variety of lines of a cubic

Multiplicative Chow-Künneth decompositions and varieties of cohomological K3 type