@article{a088cfb8f4514473a4c37d5ea5f3ddba,
title = "Embedding pointed curves in K3 surfaces",
abstract = "We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with specified cross ratios. This builds on work of Mukai and others characterizing embeddings of curves into K3 surfaces via non-abelian Brill–Noether theory. Our study leads naturally to enumerative problems, which we solve in several specific cases. These have applications to the existence of sections of del Pezzo fibrations with prescribed invariants.",
keywords = "Brill–Noether theory, K3 surfaces",
author = "Brendan Hassett and Yuri Tschinkel",
note = "Funding Information: Andrew Kresch provided invaluable assistance on this project and in particular, the computations in the enclosed appendix. We benefited from conversations with Shigeru Mukai, Frank-Olaf Schreyer, and Alessandro Verra. We are grateful to the referee for a number of suggestions, including an improvement to the proof of Theorem 4. The first author is supported by National Science Foundation Grants 0968349, 0901645, and 1148609; the second author is supported by National Science Foundation Grants 0739380, 0968349, and 1160859. Publisher Copyright: {\textcopyright} 2014, Springer-Verlag Berlin Heidelberg.",
year = "2014",
month = nov,
day = "12",
doi = "10.1007/s00209-014-1339-x",
language = "English (US)",
volume = "278",
pages = "927--953",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "3-4",
}