Publicado

2018-01-01

Deformations of Noncompact Calabi-Yau threefolds

Deformaciones de Tres-variedades Calabi-Yau no Compactas

DOI:

https://doi.org/10.15446/recolma.v1n52.74554

Palabras clave:

Calabi-Yau, Deformations of noncompact manifolds (en)
Calabi-Yau, Deformaciones de variedades no compactas (es)

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Autores/as

  • Elizabeth Gasparim Universidad Católica del Norte
  • Thomas Köppe Universidad Católica del Norte
  • Francisco Rubilar Universidad Católica del Norte
  • Bruno Suzuki Universidad Católica del Norte
We describe deformations of noncompact Calabi-Yau threefolds
Wk := Tot(OP1 (-k) ⊕ OP1 (k - 2)),
for k = 1, 2, 3. We compute deformations concretely by calculations of the cohomology group H1(Wk, TWk) via Čech cohomology. We show that for each k = 1, 2, 3 the associated structures are qualitatively different, and we also comment on their differences from the analogous structures of simpler non-compact twofolds Tot(OP1 (-k)).
Describimos deformaciones de 3-variedades Calabi-Yau no compactas
Wk := Tot(OP1 (-k) ⊕ OP1 (k - 2)),
para k = 1, 2, 3. Concretamente, calculamos las deformaciones a través del primer grupo de cohomología H1(Wk, TWk) vía cohomología de Čech. Mostramos que para cada k = 1, 2, 3 las estructuras asociadas son cualitativamente distintas y, además, comentamos sobre sus diferencias con las estructuras análogas de las 2-variedades no compactas Tot(OP1 (-k)).

Referencias

E. Ballico, S. Barmeier, E. Gasparim, L. Grama, and L.A.B. San Martin, A

Lie theoretical construction of a Landau-Ginzburg model without projective

mirrors, arXiv:1610.06965.

S. Barmeier and E. Gasparim, Classical deformations of local surfaces and

their moduli spaces of instantons, arXiv:1604.01133. (2017).

M. Bershadsky, Kodaira-Spencer theory of gravity, Quantum Field Theory

and String Theory 328 (1995), 23-38.

E. Gasparim, Holomorphic bundles on O(-k) are algebraic, Communications

in Algebra 25(9) (1997), 3001-3009.

R. Hartshorne, Algebraic Geometry, graduate texts in mathematics, no.52. ed., Springer-Verlag, New York, 1977.

J. Jiménez, Contraction of nonsingular curves, Duke Math. 65 (1992), 313-332.

K. Kodaira, Complex manifolds and deformations of complex structures,

Berlin: Springer, 1986.

M. Manetti, Lectures on deformations of complex manifolds (deformations from differential graded viewpoint), vol. 7, Rend. Mat. Appl., 2004.

F. Rubilar, Deformaciones de estructuras complejas de 3-variedades Calabi-Yau, Tesis de magíster, Universidad Católica del Norte, Antofagasta, Chile, marzo 2017.

Cómo citar

APA

Gasparim, E., Köppe, T., Rubilar, F. y Suzuki, B. (2018). Deformations of Noncompact Calabi-Yau threefolds. Revista Colombiana de Matemáticas, 52(1), 41–57. https://doi.org/10.15446/recolma.v1n52.74554

ACM

[1]
Gasparim, E., Köppe, T., Rubilar, F. y Suzuki, B. 2018. Deformations of Noncompact Calabi-Yau threefolds. Revista Colombiana de Matemáticas. 52, 1 (ene. 2018), 41–57. DOI:https://doi.org/10.15446/recolma.v1n52.74554.

ACS

(1)
Gasparim, E.; Köppe, T.; Rubilar, F.; Suzuki, B. Deformations of Noncompact Calabi-Yau threefolds. rev.colomb.mat 2018, 52, 41-57.

ABNT

GASPARIM, E.; KÖPPE, T.; RUBILAR, F.; SUZUKI, B. Deformations of Noncompact Calabi-Yau threefolds. Revista Colombiana de Matemáticas, [S. l.], v. 52, n. 1, p. 41–57, 2018. DOI: 10.15446/recolma.v1n52.74554. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/74554. Acesso em: 29 mar. 2024.

Chicago

Gasparim, Elizabeth, Thomas Köppe, Francisco Rubilar, y Bruno Suzuki. 2018. «Deformations of Noncompact Calabi-Yau threefolds». Revista Colombiana De Matemáticas 52 (1):41-57. https://doi.org/10.15446/recolma.v1n52.74554.

Harvard

Gasparim, E., Köppe, T., Rubilar, F. y Suzuki, B. (2018) «Deformations of Noncompact Calabi-Yau threefolds», Revista Colombiana de Matemáticas, 52(1), pp. 41–57. doi: 10.15446/recolma.v1n52.74554.

IEEE

[1]
E. Gasparim, T. Köppe, F. Rubilar, y B. Suzuki, «Deformations of Noncompact Calabi-Yau threefolds», rev.colomb.mat, vol. 52, n.º 1, pp. 41–57, ene. 2018.

MLA

Gasparim, E., T. Köppe, F. Rubilar, y B. Suzuki. «Deformations of Noncompact Calabi-Yau threefolds». Revista Colombiana de Matemáticas, vol. 52, n.º 1, enero de 2018, pp. 41-57, doi:10.15446/recolma.v1n52.74554.

Turabian

Gasparim, Elizabeth, Thomas Köppe, Francisco Rubilar, y Bruno Suzuki. «Deformations of Noncompact Calabi-Yau threefolds». Revista Colombiana de Matemáticas 52, no. 1 (enero 1, 2018): 41–57. Accedido marzo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/74554.

Vancouver

1.
Gasparim E, Köppe T, Rubilar F, Suzuki B. Deformations of Noncompact Calabi-Yau threefolds. rev.colomb.mat [Internet]. 1 de enero de 2018 [citado 29 de marzo de 2024];52(1):41-57. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/74554

Descargar cita

CrossRef Cited-by

CrossRef citations5

1. Edoardo Ballico, Elizabeth Gasparim, Bruno Suzuki. (2021). Infinite dimensional families of Calabi–Yau threefolds and moduli of vector bundles. Journal of Pure and Applied Algebra, 225(4), p.106554. https://doi.org/10.1016/j.jpaa.2020.106554.

2. Severin Barmeier, Elizabeth Gasparim. (2019). Classical deformations of noncompact surfaces and their moduli of instantons. Journal of Pure and Applied Algebra, 223(6), p.2543. https://doi.org/10.1016/j.jpaa.2018.09.006.

3. Edoardo Ballico, Elizabeth Gasparim, Francisco Rubilar. (2021). 20 Open questions about deformations of compactifiable manifolds. São Paulo Journal of Mathematical Sciences, 15(2), p.661. https://doi.org/10.1007/s40863-021-00213-8.

4. E. Ballico, E. Gasparim, F. Rubilar, B. Suzuki. (2023). Birational Geometry, Kähler–Einstein Metrics and Degenerations. Springer Proceedings in Mathematics & Statistics. 409, p.263. https://doi.org/10.1007/978-3-031-17859-7_13.

5. Eduardo Ballico, Elizabeth Gasparim, Thomas Köppe, Bruno Suzuki. (2022). Poisson Structures on the Conifold and Local Calabi-Yau Threefolds. Reports on Mathematical Physics, 90(3), p.299. https://doi.org/10.1016/S0034-4877(22)00078-7.

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