@inbook{74c69b359072428a8dcc21e530ad23ab,

title = "Reduction Types of Genus-3 Curves in a Special Stratum of their Moduli Space",

abstract = "We study a 3-dimensional stratum ℳ3 , V of the moduli space ℳ3 of curves of genus 3 parameterizing curves Y that admit a certain action of V = C2 × C2. We determine the possible types of the stable reduction of these curves to characteristic different from 2. We define invariants for ℳ3 , V and characterize the occurrence of each of the reduction types in terms of them. We also calculate the j-invariant (respectively the Igusa invariants) of the irreducible components of positive genus of the stable reduction Y in terms of the invariants.",

keywords = "Dixmier–Ohno invariants, Plane quartic curves, Stable reduction",

author = "Irene Bouw and Nirvana Coppola and Pınar Kılı{\c c}er and Sabrina Kunzweiler and Garc{\'i}a, {Elisa Lorenzo} and Anna Somoza",

note = "Funding Information: This project began at the Women in Numbers Europe 3 workshop in Rennes, August 2019. We are grateful to the organizers for bringing us together and providing us with an excellent working environment to get this project underway. We thank Christophe Ritzenthaler for his ideas for the proofs of Propositions 5, 6, 8, and 9. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-77700-5_4",

language = "English",

isbn = "978-3-030-77699-2",

series = "Association for Women in Mathematics Series",

publisher = "Springer",

pages = "115--162",

editor = "Cojocaru, {Alina Carmen } and Ionica, {Sorina } and Garc{\'i}a, {Elisa Lorenzo }",

booktitle = "Women in Numbers Europe III",

}