On T‐divisors and intersections in the moduli space of stable surfaces M¯1,3$\overline{\mathfrak {M}}_{1,3}

The moduli space of stable surfaces with KX2=1$K_X^2 = 1$ and χ(X)=3$\chi (X) = 3$ has at least two irreducible components that contain surfaces with T‐singularities. We show that the two known components intersect transversally in a divisor. Moreover, we exhibit other new boundary divisors and stud...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2023-02, Vol.107 (2), p.750-776
Main Authors: Coughlan, Stephen, Franciosi, Marco, Pardini, Rita, Rana, Julie, Rollenske, Sönke
Format: Article
Language:English
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Summary:The moduli space of stable surfaces with KX2=1$K_X^2 = 1$ and χ(X)=3$\chi (X) = 3$ has at least two irreducible components that contain surfaces with T‐singularities. We show that the two known components intersect transversally in a divisor. Moreover, we exhibit other new boundary divisors and study how they intersect one another.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12696