Work

Movable cones of complete intersections of multidegree one on products of projective spaces

Year: 2024

Type: article

Abstract: We study Calabi–Yau manifolds which are complete intersections of hypersurfaces of multidegree 1 in an m-fold product of n-dimensional projective spaces. Using the theory of Coxeter groups, we show that the birational automorphism group of such a Calabi–Yau manifold X is infinite and a free product of copies of $${\mathbb {Z}}$$ Z . Moreover, we give an explicit description of the boundary of the movable cone $${{\,\mathrm{{\overline{Mov}}}\,}}(X)$$ Mov ¯ ( X ) . In the end, we consider examples for the general and non-general case and picture the movable cone and the fundamental domain for the action of $${{\,\textrm{Bir}\,}}(X)$$ Bir ( X ) .

Source: Selecta Mathematica

DOI: 10.1007/s00029-024-01005-6

Authors: Michael Hoff, Isabel Stenger, José Ignacio Yáñez

Institutions: Leibniz University Hannover, University of California, Los Angeles

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Science Foundation, Deutsche Forschungsgemeinschaft, Universität des Saarlandes