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Automorphisms of Nikulin-type orbifolds

Simon Brandhorst, Grégoire Menet, Stevell Muller

Abstract

We show that the monodromoy group of Nikulin-type orbifolds is maximal and classify finite order symplectic automorphisms up to deformation in terms of their action on the second integral cohomology group.

Automorphisms of Nikulin-type orbifolds

Abstract

We show that the monodromoy group of Nikulin-type orbifolds is maximal and classify finite order symplectic automorphisms up to deformation in terms of their action on the second integral cohomology group.

Paper Structure

This paper contains 14 sections, 17 theorems, 24 equations, 1 table.

Table of Contents

  1. Introduction
  2. Reminders and notation
  3. Lattices
  4. Orbifolds of Nilukin-type
  5. Beauville--Bogomolov form
  6. Period map and moduli space
  7. The monodromy group
  8. Reflections as monodromy operators
  9. The orthogonal group of the discriminant form.
  10. Generation of the monodromy group by reflections
  11. Classification of symplectic birational automorphisms
  12. Torelli setting
  13. Results and comments
  14. Classification of standard symplectic automorphisms

Key Result

Theorem 1.1

Let $X$ be an irreducible symplectic orbifold of Nikulin-type and $\mathop{\mathrm{Mon}}\nolimits^2(X)$ its monodromy group. Then

Theorems & Definitions (48)

  • Theorem 1.1
  • Remark 1.2
  • Remark 1.3
  • Definition 2.1
  • Remark 2.3
  • Definition 2.4
  • Theorem 2.5: Ulrike2
  • Remark 2.6
  • Remark 2.8
  • Proposition 2.10: Lol4
  • ...and 38 more