arXiv subjects

R. Pandharipande

Publications and source records attributed to R. Pandharipande.

76 records · Page 5Linked to original sources

arXiv1995

A Geometric Invariant Theory Compactification of M_{g,n} Via the Fulton-MacPherson Configuration Space

A compactification over $\overline{M}_g$ of $M_{g,n}$ is obtained by considering the relative Fulton-MacPherson configuration space of the universal curve. The resulting compactification differs from the Deligne-Mumford space $\overline{M}_{g,n}$. In case $n=2$, the compactification constructed here and the Deligne-Mumford compactification are essentially the distinct minimal resolutions of the fiber product over $\overline{M}_g$ of the universal curve with itself.

alg-geom↗

arXiv1995

Severi Degrees in Cogenus 3

In this short note, a new computation of the degree of the locus of 3-nodal plane curves in the linear system of degree d plane curves is given. The answer is expressed as a tautological class on a blow-up of the Hilbert scheme of 3 points in the plane. The class is evaluated by the Bott residue formula.

alg-geom↗

arXiv1995

Intersections of Q-Divisors on Kontsevich's Moduli Space $\bar{M}_{0,n}(P^r,d)$ and Enumerative Geometry

The theory of Q-Cartier divisors on the space of n-pointed, genus 0, stable maps to projective space is considered. Generators and Picard numbers are computed. A recursive algorithm computing all top intersection products of Q-Divisors is established. As a corollary, an algorithm computing all characteristic numbers of rational curves in P^r is proven (including simple tangency conditions). Computations of these characteristic numbers are carried out in many examples. The degree of the 1-cuspidal rational locus in the linear system of degree d plane curves is explicitly evaluated.

alg-geom↗

arXiv1995

A Compactification Over $\overline{M}_g$ Of The Universal Moduli Space of Slope-Semistable Vector Bundles

A projective moduli space of pairs (C,E) where E is a slope- semistable torsion free sheaf of uniform rank on a Deligne- Mumford stable curve C is constructed via G.I.T. There is a natural SL x SL action on the relative Quot scheme over the universal curve of the Hilbert scheme of pluricanonical, genus g curves. The G.I.T. quotient of this product action yields a functorial, compact solution to the moduli problem of pairs (C,E). Basic properties of the moduli space are studied. An alternative approach to the moduli problem of pairs has been suggested by D. Gieseker and I Morrison and completed by L. Caporaso in the rank 1 case. It is shown the contruction given here is isomorphic to Caporaso's compactification in the rank 1 case.

alg-geom↗