2017/11/27 by Cristian Minoccheri, Minoccheri, Cristian, Xuanyu Pan +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1711.09987
openalex publication_date 2017/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove results about 1-cycles on certain Fano varieties using techniques that rely on rational curves. Firstly, we show that Fano weighted complete intersections with index bigger than half their dimension have trivial first Griffiths group. Secondly, we prove that the first Chow group of most 2-Fano weighted complete intersections, and of 2-Fano conic-connected varieties in ℙn of high enough index (with 3 obvious exceptions), are generated by lines. Furthermore, if the Fano variety of lines is irreducible, the first Chow group is isomorphic to ℤ.