Configurations of points on degenerate varieties and properness of moduli spaces

  • Dan Abramovich

    Brown University, Providence, USA
  • Barbara Fantechi

    SISSA, Trieste, Italy
Configurations of points on degenerate varieties and properness of moduli spaces cover
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Abstract

We generalize Kim and Sato's construction of the relative configuration space to the case where is an algebraic stack; and construct an analogous projective moduli space for a degeneration . We construct and 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.

Cite this article

Dan Abramovich, Barbara Fantechi, Configurations of points on degenerate varieties and properness of moduli spaces. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 1–17

DOI 10.4171/RSMUP/137-1