New York Journal of Mathematics
Volume 25 (2019), 168-173


Xi Chen

Nodal curves on K3 surfaces

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Published: January 20, 2019.
Keywords: K3 surface, severi variety, moduli space of curves.
Subject: Primary 14J28; Secondary 14E05.

In this paper, we study the Severi variety VL,g of genus g curves in |L| on a general polarized K3 surface (X,L). We show that the closure of every component of VL,g contains a component of VL,g-1. As a consequence, we see that the general members of every component of VL,g are nodal.


Research partially supported by Discovery Grant 262265 from the Natural Sciences and Engineering Research Council of Canada.

Author information

Xi Chen:
632 Central Academic Building
University of Alberta
Edmonton, Alberta T6G 2G1, CANADA