Timeline for Smoothness of space of morphisms from a curve to a locally complete intersection
Current License: CC BY-SA 3.0
4 events
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| Jun 13, 2017 at 8:22 | comment | added | Jason Starr | "For example, are they smooth?" For fixed $g>1$, $r$ and $d$, for every integer $1\leq s \leq r$, by Gieseker-Petri, for a sufficiently general curve $C$ of genus $g$, the scheme $\mathcal{G}^s_d(C)$ parameterizing linear systems on $C$ of degree $d$ and (projective) dimension $s$ is smooth. There is a Grassmannian bundle over an open subscheme of $\mathcal{G}^s_d(C)$ that embeds into $\text{Hom}^d(C,\mathbb{P}^r)$. Thus, there is a smooth stratification. | |
| Jun 9, 2017 at 20:21 | comment | added | user312073 | Thank you very much for your answer! Just out of curiosity: can one say anything about the components of $\text{Hom}(C,\mathbb P^2)$? For example, are they smooth? And in general, are the components of $\text{Hom}(C,Y)$ smooth? | |
| S Jun 9, 2017 at 20:08 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Jun 9, 2017 at 20:08 | history | made wiki | Post Made Community Wiki by Jason Starr |