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Transactions of the American Mathematical Society

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Reduced invariants from cuspidal maps


Authors: Luca Battistella, Francesca Carocci and Cristina Manolache
Journal: Trans. Amer. Math. Soc. 373 (2020), 6713-6756
MSC (2010): Primary 14N35
DOI: https://doi.org/10.1090/tran/8141
Published electronically: June 24, 2020
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Abstract: We consider genus one enumerative invariants arising from the Smyth-Viscardi moduli space of stable maps from curves with nodes and cusps. We prove that these invariants are equal to the reduced genus one invariants of the quintic threefold, providing a modular interpretation of the latter.


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Additional Information

Luca Battistella
Affiliation: Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Germany
Email: lbattistella@mathi.uni-heidelberg.de

Francesca Carocci
Affiliation: School of Mathematics, University of Edinburgh, Scotland
Email: Francesca.Carocci@ed.ac.uk

Cristina Manolache
Affiliation: School of Mathematics and Statistics, University of Sheffield, United Kingdom
MR Author ID: 818812
Email: C.Manolache@shef.ac.uk

DOI: https://doi.org/10.1090/tran/8141
Received by editor(s): April 7, 2018
Received by editor(s) in revised form: February 10, 2020
Published electronically: June 24, 2020
Additional Notes: The first author was supported by a Royal Society 1st Year URF and DHF Research Grant Scheme.
The third author was supported by an EPSRC funded Royal Society Dorothy Hodgkin Fellowship.
This work was supported by the Engineering and Physical Sciences Research Council grant EP/L015234/1: the EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface.
Article copyright: © Copyright 2020 American Mathematical Society