arXiv subjects

Alberto Collino

Publications and source records attributed to Alberto Collino.

6 recordsLinked to original sources

arXiv2013

On the life and scientific work of Gino Fano

A collection of selected papers of Gino Fano, containing most of his research papers in Italian, is now available on line at the site of Biblioteca Digitale Italiana di Matematica. The address is: http://www.bdim.eu/ The realization of this collection on line is part of a joint project of Unione Matematica Italiana (UMI) and Societa' Italiana per la Matematica Applicata e Industriale (SIMAI). The present submission to arXiv is the introduction to the collection and an announcement of it as well.

math.HO↗

arXiv2012

Remarks On the Topology of the Fano surface

We analize the semistable degeneration of the Fano surface F when the cubic threefold becomes the Segre primal. This gives an explicit topological decomposition for F. The decomposition is used to decide that the Fano surface is not an an Eilenberg Mac-Lane K(\pi,1) space, this was the question that prompted us to look into the matter.

math.AG↗

arXiv2002

On K_1 and K_2 of algebraic surfaces

We study the higher Chow groups $CH^2(X,1)$ and $CH^3(X,2)$ of smooth, projective algebraic surfaces over a field of char 0. We develop a theoretical framework to study them by using so-called higher normal functions and higher infinitesimal invariants when the cycles are supported on normal crossing divisors. Then we investigate their structure on hypersurfaces in projective 3-space. This leads to vanishing or decomposbility results. On the other hand we find examples of these groups in degrees 4 and 5 where the result is a highly indecomposably (hence big) abelian group. Part of the examples are due to Alberto Collino.

math.AG↗

arXiv2000

Indecomposable Higher Chow cycles on Jacobians

We construct some natural cycles with trivial regulator in the higher Chow groups of Jacobians. For hyperelliptic curves we use a criterion due to J. Lewis to prove that the cycles we construct are indecomposable, and then use a specialization argument to prove indecomposability for more general curves. Please note that math.AG/9909062 has become an obsolete version of some of the results in the present paper.

math.AG↗

arXiv1999

Indecomposable Higher Chow Cycles on Low Dimensional Jacobians

Title: Indecomposable Higher Chow Cycles on Low Dimensional Jacobians Authors: Alberto Collino Comments: AMS-TeX, 10 pages Subj-class: Algebraic Geometry MSC-class: 14C30 ;19E15 There is a basic indecomposable higher cycle K in Bloch's higher Chow group CH^{g}(J(C),1) on the Jacobian J(C) of a general hyperelliptic curve C of genus g. Consider K(t) the translation of K associated with a point t in C, we prove that in general K - K(t) is indecomposable if the genus is at least 3. Our tool is Lewis' condition for indecomposability. We show next that on the jacobian J(C) of a general curve C of genus 3 there is a geometrically natural family of higher cycles, when C becomes hyperelliptic the family in the limit contains a component of indecomposable cycles of type K - K(t).

math.AG↗

arXiv1993

On the Griffiths group of the cubic sevenfold

We prove that the Griffiths group of 3-cycles homologous to zero modulo algebraic equivalence, on a generic hypersurfaces of dimension 7 and degree 3 is not finitely generated, even when tensored with Q. Using this and a result of Nori, we give examples of varieties for which some Griffiths group is not finitely generated (modulo torsion) but whose corresponding intermediate Jacobian is trivial.

alg-geom↗