A Compactification of the Space of Holomorphic Maps from $¶^1$ into $¶^r$
| dc.creator | Lin, Jiayuan | |
| dc.date | 2005-05-23 | |
| dc.date | 2005-05-25 | |
| dc.date.accessioned | 2026-07-07T05:20:11Z | |
| dc.date.available | 2026-07-07T05:20:11Z | |
| dc.description | Let $M_{d}(¶^r)$ be the space of $(r+1)$-tuples $(f_0,...,f_r)$ modulo homothety, where $f_0,...,f_r$ are homogeneous polynomials of degree $d$ in two variables. Let $M_{d}^{\circ}(¶^r)$ be the open subset of $M_{d}(¶^r)$ such that $f_0,...,f_r$ have no common zeros. Then $M_{d}^{\circ}(¶^r)$ parametrizes the space of holomorphic maps of degree $d$ from $¶^1$ into $¶^r$. In general the boundary divisor $M_{d}(¶^r) \setminus M_{d}^{\circ}(¶^r)$ is not normal crossing. In this paper we will give a natural stratification of this boundary and show that we can process an iterated blow-ups along these strata (or its proper transformations) to obtain a compactification of $M_{d}^{\circ}(¶^n)$ with normal crossing divisors. | |
| dc.description | 25 pages, typos corrected, more precise reference added | |
| dc.identifier | https://arxiv.org/abs/math/0505482 | |
| dc.identifier | http://arxiv.org/abs/math/0505482 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75286 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C05; 14J17; 14E15 | |
| dc.title | A Compactification of the Space of Holomorphic Maps from $¶^1$ into $¶^r$ | |
| dc.type | text |