Index of coregularity zero log Calabi–Yau pairs

Filipazzi, Stefano; Mauri, Mirko; Moraga, Joaquín

doi:10.2140/ant.2025.19.383

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Index of coregularity zero log Calabi–Yau pairs

Stefano Filipazzi, Mirko Mauri and Joaquín Moraga

Vol. 19 (2025), No. 2, 383–413

DOI: 10.2140/ant.2025.19.383

Abstract

We study the index of log Calabi–Yau pairs $(X, B)$ of coregularity 0. We show that $2 λ (K_{X} + B) \sim 0$ , where $λ$ is the Weil index of $(X, B)$ . This is in contrast to the case of klt Calabi–Yau varieties, where the index can grow doubly exponentially with the dimension. Our sharp bound on the index extends to the context of generalized log Calabi–Yau pairs, semi-log canonical pairs, and isolated log canonical singularities of coregularity 0. As a consequence, we show that the index of a variety appearing in the Gross–Siebert program or in the Kontsevich–Soibelman program is at most $2$ . Finally, we discuss applications to Calabi–Yau varieties endowed with a finite group action, including holomorphic symplectic varieties endowed with a purely nonsymplectic automorphism.

Keywords

Calabi–Yau, index conjecture, dual complex, minimal model program, mirror symmetry

Mathematical Subject Classification

Primary: 14B05, 14E30, 14J32

Milestones

Received: 30 May 2023

Revised: 10 November 2023

Accepted: 5 March 2024

Published: 31 January 2025

Authors

Stefano Filipazzi
EPFL, SB MATH CAG Lausanne Switzerland

Mirko Mauri
École Polytechnique Palaiseau France

Joaquín Moraga
Department of Mathematics UCLA Los Angeles, CA United States

Open Access made possible by participating institutions via Subscribe to Open.

Vol. 19, No. 2, 2025