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𝔸-curves on log smooth varieties

  • Qile Chen ORCID logo EMAIL logo and Yi Zhu ORCID logo
Published/Copyright: July 19, 2017

Abstract

In this paper, we study 𝔸1-connected varieties from log geometry point of view, and prove a criterion for 𝔸1-connectedness. As applications, we provide many interesting examples of 𝔸1-connected varieties in the case of complements of ample divisors, and the case of homogeneous spaces. We also obtain a logarithmic version of Hartshorne conjecture characterizing projective spaces and affine spaces.

Award Identifier / Grant number: DMS-1403271

Award Identifier / Grant number: DMS-1560830

Funding statement: Qile Chen is partially supported by the Simons Foundation and NSF (grants DMS-1403271, DMS-1560830).

Acknowledgements

We are grateful to Professor Dan Abramovich, Steffen Marcus, and Jonathan Wise for useful discussions on log étale resolution. In the collaboration with them on [3], we learned the idea of log étale descent, which greatly inspires our construction in the current paper. During the preparation of this paper, we received a lot of help from Johan de Jong, Yi Hu, Mathieu Huruguen, János Kollár, Jason Starr, Michael Thaddeus, and Xinwen Zhu. We would like to express our thanks to them. A large part of our work has been done during the first named author’s visit of the Math Department at the University of Utah in February 2014. We would like to thank the Utah Math Department for its hospitality.

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Received: 2015-06-24
Revised: 2017-05-23
Published Online: 2017-07-19
Published in Print: 2019-11-01

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