COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Algebraic Geometry Seminar > k-gonal loci in Severi varieties of curves on K3 surfaces and rational curves on hyperkahler manifolds

## k-gonal loci in Severi varieties of curves on K3 surfaces and rational curves on hyperkahler manifoldsAdd to your list(s) Download to your calendar using vCal - Andreas Knutsen (Bergen)
- Wednesday 01 May 2013, 14:15-15:15
- MR 13, CMS.
If you have a question about this talk, please contact Dr. J Ross. This is a report on recent joint work with C. Ciliberto. Let $(S,H)$ be a general primitively polarized complex K3 surface of genus $p$ and consider the Severi varieties $V_{|H|,\delta}$ parametrizing $\delta$- nodal curves in the linear system $|H|$, for $0 \leq \delta \leq p$. It is well-known that these are smooth and nonempty of dimension $p-\delta$. We consider the subloci V(k,|H|,\delta) of curves whose normalizations possess a g1k. We give necessary and sufficient conditions depending on $p$, $\delta$ and $k$ for these loci to be nonempty, and prove that, when nonempty, there is always an irreducible component of the expected dimension. In contrast to the case of smooth curves, the Severi varieties thus contain proper subloci of gonalities lower than the maximal gonality given by Brill-Noether theory. I will also discuss applications to the study of the Mori cone of rational curves in the punctual Hilbert scheme Hilb(k,S)$, since the curves in V(k,|H|,\delta) naturally induce rational curves in \Hilb(k,S)$. This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- MR 13, CMS
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsNumber Theory Study Group: Langlands correspondence Engineers Without Borders Special Lecture Series: THE NATURAL COOK: A THEORY OF HUMAN EVOLUTION Major Public Lectures in Cambridge Cambridge Energy Conference Dr T. Ferrus## Other talksUnbiased Estimation of the Eigenvalues of Large Implicit Matrices Mechanistic model development to characterise drug effects on platelets over time in pharmaceutical research. Using Inclusive Design to Focus on User Experience (UX) Lung Cancer. Part 1. Patient pathway and Intervention. Part 2. Lung Cancer: Futurescape New Insights in Immunopsychiatry (Provisional Title) Graded linearisations for linear algebraic group actions Molecular mechanisms of cardiomyopathies in patients with severe non-ischemic heart failure Retinal mechanisms of non-image-forming vision Making a Crowdsourced Task Attractive: Measuring Workers Pre-task Interactions |