Year: 2025
Type: letter
Abstract: Constant cycle curves on a K3 surface X over $${\mathbb C}$$ C are curves whose points all define the same class in the Chow group. In this paper we study correspondences $$Z \subseteq X\times X$$ Z ⊆ X × X over $${\mathbb C}$$ C acting on the group $${{\,\textrm{ccc}\,}}(X)$$ ccc ( X ) of cycles generated by irreducible constant cycle curves. We construct for any $$n\ge 2$$ n ≥ 2 and any very ample line bundle L a locus $$Z_n(L)\subseteq X\times X$$ Z n ( L ) ⊆ X × X which is expected to have dimension 2 and which yields a correspondence that acts on $${{\,\textrm{ccc}\,}}(X)$$ ccc ( X ) , when it has dimension 2. We provide examples of $$Z_n(L)$$ Z n ( L ) for low n and exhibit one correspondence different from $$Z_n(L)$$ Z n ( L ) acting on $${{\,\textrm{ccc}\,}}(X)$$ ccc ( X ) .
Source: Mathematische Zeitschrift
Author: Sara Torelli
Institution: Politecnico di Milano
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4416088550