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New York Journal of Mathematics
Volume 26 (2020), 138-148

  

Massimo Bagnarol, Barbara Fantechi, and Fabio Perroni

On the motive of Quot schemes of zero-dimensional quotients on a curve

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Published: February 3, 2020.
Keywords: Quot schemes; Grothendieck ring of varieties.
Subject: 14D20, 14H60.

Abstract
For any locally free coherent sheaf on a fixed smooth projective curve, we study the class, in the Grothendieck ring of varieties, of the Quot scheme that parametrizes zero-dimensional quotients of the sheaf. We prove that this class depends only on the rank of the sheaf and on the length of the quotients. As an application, we obtain an explicit formula that expresses it in terms of the symmetric products of the curve.

Acknowledgements

The first author was supported by a Ph.D. Fellowship in Geometry and Mathematical Physics at SISSA. The second and third author were supported by the national projects PRIN 2015EYPTSB-PE1 "Geometria delle varietá algebriche" and 2017SSNZAW 005-PE1 "Moduli Theory and Birational Classification", and by the research group GNSAGA of INDAM. The third author was also supported by FRA 2018 of the University of Trieste.


Author information

Massimo Bagnarol:
SISSA -- International School for Advanced Studies
via Bonomea 265, 34136 Trieste, Italy

mbagnarol@sissa.it

Barbara Fantechi:
SISSA -- International School for Advanced Studies
via Bonomea 265, 34136 Trieste, Italy

fantechi@sissa.it

Fabio Perroni:
Dipartimento di Matematica e Geoscienze
UniversitÓ degli Studi di Trieste
via Valerio 12/1, 34127 Trieste, Italy

fperroni@units.it