Configurations of points on degenerate varieties and properness of moduli spaces
Rendiconti del Seminario Matematico della Università di Padova, Tome 137 (2017), pp. 1-17.

We generalize Kim and Sato's construction of the relative configuration space X D [n] to the case where X is an algebraic stack; and construct an analogous projective moduli space W π [n] for a degeneration π:WB. We construct X D [n] and W π [n] and prove their properness using a universal construction of expanded degenerations and pairs introduced in our paper with Cadman and Wise. We use these spaces to re-prove the properness of Jun Li’s moduli of relative and degenerate stable maps, and generalize this properness result to the case of target stacks.

DOI : 10.4171/RSMUP/137-1
Classification : 14
Mots clés : Moduli spaces, algebraic stacks, Gromov–Witten invariants, configuration spaces
Abramovich, Dan 1 ; Fantechi, Barbara 2

1 Brown University, PROVIDENCE, UNITED STATES
2 SISSA, TRIESTE, ITALY
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     title = {Configurations of points on degenerate varieties and properness of moduli spaces},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--17},
     publisher = {European Mathematical Society Publishing House},
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     volume = {137},
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     doi = {10.4171/RSMUP/137-1},
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Abramovich, Dan; Fantechi, Barbara. Configurations of points on degenerate varieties and properness of moduli spaces. Rendiconti del Seminario Matematico della Università di Padova, Tome 137 (2017), pp. 1-17. doi : 10.4171/RSMUP/137-1. http://www.numdam.org/articles/10.4171/RSMUP/137-1/

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