Algebra & Number Theory
- Algebra Number Theory
- Volume 14, Number 4 (2020), 907-926.
Deformations of smooth complete toric varieties: obstructions and the cup product
Let be a complete -factorial toric variety. We explicitly describe the space and the cup product map in combinatorial terms. Using this, we give an example of a smooth projective toric threefold for which the cup product map does not vanish, showing that in general, smooth complete toric varieties may have obstructed deformations.
Algebra Number Theory, Volume 14, Number 4 (2020), 907-926.
Received: 2 January 2019
Revised: 25 November 2019
Accepted: 6 February 2020
First available in Project Euclid: 30 June 2020
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14B12: Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10] 14D15: Formal methods; deformations [See also 13D10, 14B07, 32Gxx]
Ilten, Nathan; Turo, Charles. Deformations of smooth complete toric varieties: obstructions and the cup product. Algebra Number Theory 14 (2020), no. 4, 907--926. doi:10.2140/ant.2020.14.907. https://projecteuclid.org/euclid.ant/1593482422