arXiv subjects

Carel Faber

Publications and source records attributed to Carel Faber.

23 records · Page 2Linked to original sources

arXiv1999

Plane curves with small linear orbits I

The `linear orbit' of a plane curve of degree d is its orbit in the projective space of dimension d(d+3)/2 parametrizing such curves under the natural action of PGL(3). In this paper we compute the degree of the closure of the linear orbits of most curves with positive dimensional stabilizers. Our tool is a nonsingular variety dominating the orbit closure, which we construct by a blow-up sequence mirroring the sequence yielding an embedded resolution of the curve. The results given here will serve as an ingredient in the computation of the analogous information for arbitrary plane curves. Linear orbits of smooth plane curves are studied in [A-F1].

math.AG↗

arXiv1997

Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians

We describe algorithms for computing the intersection numbers of divisors and of Chern classes of the Hodge bundle on the moduli spaces of stable pointed curves. We also discuss the implementations and the results obtained. There are several applications. We discuss one in particular: the calculation of the projection in the tautological ring of the moduli space of abelian varieties of the class of the locus of Jacobians.

alg-geom↗

arXiv1995

Intersection-theoretical computations on \Mgbar

We determine necessary conditions for ample divisors in arbitrary genus as well as for very ample divisors in genus 2 and 3. We also compute the intersection numbers $λ^9$ and $λ_{g-1}^3$ in genus 4. The latter number is relevant for counting curves of higher genus on manifolds, cf. the recent work of Bershadsky et al.

alg-geom↗

arXiv1992

Linear orbits of smooth plane curves

The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits of smooth curves under this action: we construct a resolution of the closure of the orbit of a given curve, and we use it to compute its degree. This turns out to depend only on the degree of the curve, the order of its automorphism group, and on the number and type of its flexes. This paper will appear on the Journal of Algebraic Geometry.

alg-geom↗

arXiv1992

Linear orbits of d-tuples of points in P^1

The group PGL(2) of linear transformations of the projective line acts naturally on the d-dimensional projective space P^d parametrizing configurations (`d-tuples') of points on the line. In this note we are concerned with the orbits of this action of PGL(2) on P^d. The closure of each orbit is a projective subvariety of P^d of which we determine the degree, the `boundary'--i.e., the complement of an orbit in its closure--, and the multiplicity at points of the boundary. These results are used to provide a complete classification of the non-singular orbit closures, and criteria for an orbit closure to be non-singular in codimension 1.

alg-geom↗