Global properties of families of plane curves
| dc.creator | Treger, Robert | |
| dc.date | 1996-01-16 | |
| dc.date.accessioned | 2026-07-07T09:06:41Z | |
| dc.date.available | 2026-07-07T09:06:41Z | |
| dc.description | We describe degenerations of projective plane curves to curves containing a fixed line $l$ as a component, and show that $H^1({\overline V}_{n,d,m}, {\Cal O} (r))=0, r \in{\Bbb Z}$, where $V_{n,d,m}\subset {\Bbb P}^N (N = n(n+3)/2)$ is the subscheme consisting of irreducible plane curves having smooth contact of order at least m with $l$ at a fixed point p of $l$ and d nodes and no other singularities. Note: the notion of admissible schemes of plane curves, introduced for the proof of the vanishing theorem, allows us to give a recipe for calculating the Hilbert polynomial of ${\overline V}_{n,d}$ (see Sect. 4), in particular the quantum cohomology of the plane. | |
| dc.description | 21 pages, AMSTeX 2.1 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9601014 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9601014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150101 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Global properties of families of plane curves | |
| dc.type | text |