Deformations of Noncompact Calabi-Yau threefolds

Elizabeth Gasparim; Thomas Köppe; Francisco Rubilar; Bruno Suzuki

doi:10.15446/recolma.v1n52.74554

Pubblicato

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

Parole chiave:

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

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Autori

Elizabeth Gasparim Universidad Católica del Norte
Thomas Köppe Universidad Católica del Norte
Francisco Rubilar Universidad Católica del Norte
Bruno Suzuki Universidad Católica del Norte

Abstract (en)
Abstract (es)

We describe deformations of noncompact Calabi-Yau threefolds

W_k := Tot(O_P1 (-k) ⊕ O_P1 (k - 2)),

for k = 1, 2, 3. We compute deformations concretely by calculations of the cohomology group H¹(W_k, TW_k) 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(O_P1 (-k)).

Describimos deformaciones de 3-variedades Calabi-Yau no compactas

W_k := Tot(O_P1 (-k) ⊕ O_P1 (k - 2)),

para k = 1, 2, 3. Concretamente, calculamos las deformaciones a través del primer grupo de cohomología H¹(W_k, TW_k) 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(O_P1 (-k)).

Riferimenti bibliografici

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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.

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

Come citare

APA

Gasparim, E., Köppe, T., Rubilar, F. e 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. e Suzuki, B. 2018. Deformations of Noncompact Calabi-Yau threefolds. Revista Colombiana de Matemáticas. 52, 1 (gen. 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: 22 gen. 2025.

Chicago

Gasparim, Elizabeth, Thomas Köppe, Francisco Rubilar, e 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. e Suzuki, B. (2018) «Deformations of Noncompact Calabi-Yau threefolds», Revista Colombiana de Matemáticas, 52(1), pagg. 41–57. doi: 10.15446/recolma.v1n52.74554.

IEEE

[1]

E. Gasparim, T. Köppe, F. Rubilar, e B. Suzuki, «Deformations of Noncompact Calabi-Yau threefolds», rev.colomb.mat, vol. 52, n. 1, pagg. 41–57, gen. 2018.

MLA

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

Turabian

Gasparim, Elizabeth, Thomas Köppe, Francisco Rubilar, e Bruno Suzuki. «Deformations of Noncompact Calabi-Yau threefolds». Revista Colombiana de Matemáticas 52, no. 1 (gennaio 1, 2018): 41–57. Consultato gennaio 22, 2025. 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 gennaio 2018 [citato 22 gennaio 2025];52(1):41-57. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/74554

Scarica citazione

CrossRef Cited-by

5

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.