Moduli of Weierstrass fibrations with marked section
Abstract
We study the the moduli space of KSBA stable pairs $(X,sS+\sum a_i F_i)$, consisting of a Weierstrass fibration $X$, its section $S$, and some fibers $F_i$. We find a compactification which is a DM stack, and we describe the objects on the boundary. We show that the fibration in the definition of Weierstrass fibration extends to the boundary, and it is equidimensional when $s \ll 1$. We prove that there are wallcrossing morphisms when the weights $s$ and $a_i$ change. When $s=1$, this recovers the work of La Nave (arXiv:math/0205035); and a special case of the work of AscherBejleri (arXiv:1702.06107).
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 DOI:
 10.48550/arXiv.1808.03539
 arXiv:
 arXiv:1808.03539
 Bibcode:
 2018arXiv180803539I
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 41 pages, improved exposition. Comments are welcome!