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On locally factorial Fano fourfolds of Picard number two

Andreas Bäuerle, Christian Mauz

Abstract

We classify the locally factorial Fano fourfolds of Picard number two with a hypersurface Cox ring that admit an effective action of a three-dimensional torus.

On locally factorial Fano fourfolds of Picard number two

Abstract

We classify the locally factorial Fano fourfolds of Picard number two with a hypersurface Cox ring that admit an effective action of a three-dimensional torus.
Paper Structure (5 sections, 19 theorems, 54 equations, 2 figures)

This paper contains 5 sections, 19 theorems, 54 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Background on Cox rings
  3. Picard group and smoothability
  4. Proof of the main result: An example case
  5. Classification lists

Key Result

Proposition 2.5

See ADHL*Prop. 3.3.3.2. Let $X = X_g$ as in constr:hypersurface. Then the anticanonical class of $X$ is given in $K = {\rm Cl}(X)$ by

Figures (2)

  • Figure :
  • Figure :

Theorems & Definitions (39)

  • Remark 2.3
  • Remark 2.4
  • Proposition 2.5
  • Proposition 2.6
  • Lemma 2.7
  • Lemma 2.8
  • Proposition 2.9
  • proof
  • Remark 2.10
  • Remark 2.11
  • ...and 29 more