On secant loci and simple linear projections of some projective varieties
| dc.creator | Park, Euisung | |
| dc.date | 2008-08-14 | |
| dc.date.accessioned | 2026-07-07T09:56:39Z | |
| dc.date.available | 2026-07-07T09:56:39Z | |
| dc.description | In this paper, we study how simple linear projections of some projective varieties behave when the projection center runs through the ambient space. More precisely, let $X \subset ¶^r$ be a projective variety satisfying Green-Lazarsfeld's property $N_p$ for some $p \geq 2$, $q \in ¶^r$ a closed point outside of $X$, and $X_q := π_q (X) \subset ¶^{r-1}$ the projected image of $X$ from $q$. First, it is shown that the secant locus $Σ_q (X)$ of $X$ with respect to $q$, i.e. the set of all points on $X$ spanning secant lines passing through $q$, is either empty or a quadric in a subspace of $¶^r$. This implies that the finite morphism $π_q : X \to X_q$ is birational. Our main result is that cohomological and local properties of $X_q$ are precisely determined by $Σ_q (X)$. To complete this result, the next step should be to classify all possible secant loci and to decompose the ambient space via the classification of secant loci. We obtain such a decomposition for Veronese embeddings and Segre embeddings. Also as an application of the main result, we study cohomological properties of low degree varieties. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0808.2005 | |
| dc.identifier | http://arxiv.org/abs/0808.2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167055 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14N15; 51N35 | |
| dc.title | On secant loci and simple linear projections of some projective varieties | |
| dc.type | text |