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On the algebraic stringy Euler number

Authors: Victor Batyrev and Giuliano Gagliardi
Journal: Proc. Amer. Math. Soc. 146 (2018), 29-41
MSC (2010): Primary 14E30; Secondary 14E15, 14E18, 14L30, 14M27
Published electronically: July 28, 2017
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Abstract: We are interested in stringy invariants of singular projective algebraic varieties satisfying a strict monotonicity with respect to elementary birational modifications in the Mori program. We conjecture that the algebraic stringy Euler number is one of such invariants. In the present paper, we prove this conjecture for varieties having an action of a connected algebraic group $ G$ and admitting equivariant desingularizations with only finitely many $ G$-orbits. In particular, we prove our conjecture for arbitrary projective spherical varieties.

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Additional Information

Victor Batyrev
Affiliation: Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Giuliano Gagliardi
Affiliation: Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

Received by editor(s): November 28, 2016
Received by editor(s) in revised form: January 25, 2017
Published electronically: July 28, 2017
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 by the authors

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