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Quasismooth hypersurfaces in toric varieties


Authors: Michela Artebani, Paola Comparin and Robin Guilbot
Journal: Proc. Amer. Math. Soc. 147 (2019), 4565-4579
MSC (2010): Primary 14M25, 14J32, 14J17, 32S25
DOI: https://doi.org/10.1090/proc/14515
Published electronically: August 7, 2019
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Abstract: We provide a combinatorial characterization of monomial linear systems on toric varieties whose general member is quasismooth. This is given both in terms of the Newton polytope and in terms of the matrix of exponents of a monomial basis.


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Additional Information

Michela Artebani
Affiliation: Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: martebani@udec.cl

Paola Comparin
Affiliation: Departamento de Matemática y Estadística, Universidad de La Frontera, Av. Francisco Salazar 1145, Temuco, Chile
Email: paola.comparin@ufrontera.cl

Robin Guilbot
Affiliation: Faculty of Mathematics, Computer Science and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
Email: rguilbot@math.cnrs.fr

DOI: https://doi.org/10.1090/proc/14515
Keywords: Toric variety, quasismooth, Newton polytope, Calabi-Yau variety
Received by editor(s): March 1, 2018
Received by editor(s) in revised form: December 10, 2018
Published electronically: August 7, 2019
Additional Notes: The first author was partially supported by Proyecto Fondecyt Regular N. 1130572 and Proyecto Anillo ACT 1415 PIA Conicyt.
The second author was partially supported by Proyecto Fondecyt Postdoctorado N. 3150015 and Proyecto Anillo ACT 1415 PIA Conicyt.
The third author was supported by the NCN project 2013/08/A/ST1/00804.
Communicated by: Alexander Braverman
Article copyright: © Copyright 2019 American Mathematical Society