We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure [email protected]
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
The Severi variety $V_{d,n}$ of plane curves of a given degree $d$ and exactly $n$ nodes admits a map to the Hilbert scheme $\mathbb{P}^{2[n]}$ of zero-dimensional subschemes of $\mathbb{P}^{2}$ of degree $n$. This map assigns to every curve $C\in V_{d,n}$ its nodes. For some $n$, we consider the image under this map of many known divisors of the Severi variety and its partial compactification. We compute the divisor classes of such images in $\text{Pic}(\mathbb{P}^{2[n]})$ and provide enumerative numbers of nodal curves. We also answer directly a question of Diaz–Harris [‘Geometry of the Severi variety’, Trans. Amer. Math. Soc.309 (1988), 1–34] about whether the canonical class of the Severi variety is effective.
Recommend this
Email your librarian or administrator to recommend adding this to your organisation's collection.