Volume 21, issue 2 (2017)

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Modular operads of embedded curves

Satoshi Kondo, Charles Siegel and Jesse Wolfson

Geometry & Topology 21 (2017) 903–922
Abstract

For each $k\ge 5$, we construct a modular operad ${\overline{\mathsc{ℰ}}}^{k}$ of “$k$–log-canonically embedded” curves. We also construct, for $k\ge 2$, a stable cyclic operad ${\overline{\mathsc{ℰ}}}_{c}^{k}$ of such curves, and, for $k\ge 1$, a cyclic operad ${\overline{\mathsc{ℰ}}}_{0,c}^{k}$ of “$k$–log-canonically embedded” rational curves.

Keywords
modular operad, log-canonical Hilbert scheme
Primary: 14H10
Secondary: 18D50
Publication
Received: 18 August 2014
Revised: 4 May 2016
Accepted: 8 May 2016
Published: 17 March 2017
Proposed: Lothar Göttsche
Seconded: Jim Bryan, Dan Abramovich
Authors
 Satoshi Kondo Faculty of Mathematics Higher School of Economics National Research University 6 Usacheva Str. Moscow 119048 Russia Charles Siegel Pacific Northwest National Laboratory 902 Battelle Blvd Richland, WA 99354 United States Jesse Wolfson Department of Mathematics University of Chicago 5734 S University Ave. Chicago, IL 60637 United States