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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.52 no.1 Bogotá Jan./June 2018

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

Original articles

Deformations of Noncompact Calabi-Yau threefolds

Deformaciones de Tres-variedades Calabi-Yau no Compactas

Elizabeth Gasparim1 

Thomas Köppe2 

Francisco Rubilar3 

Bruno Suzuki4  * 

1 Universidad Católica del Norte, Antofagasta - Chile

2 Universidad Católica del Norte, Antofagasta - Chile

3 Universidad Católica del Norte, Antofagasta - Chile

4 Universidad Católica del Norte, Antofagasta - Chile


Abstract:

We describe deformations of noncompact Calabi-Yau threefolds 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 noncompact twofolds Tot(OP1(-k)).

Keywords: Calabi-Yau; Deformations of noncompact manifolds

Resumen:

Describimos deformaciones de 3-variedades Calabi-Yau no compactas 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(OP1(-k)).

Palabras clave: Calabi-Yau; Deformaciones de variedades no compactas

Text complete end PDF

References

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2. Barmeier, S., Gasparim, E., Classical deformations of local surfaces and their moduli spaces of instantons, arXiv:1604.01133. (2017). [ Links ]

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4. Gasparim, E., Holomorphic bundles on O(-k) are algebraic, Communications in Algebra 25(9) (1997), 3001-3009. [ Links ]

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7. Kodaira, K., Complex manifolds and deformations of complex structures, Berlin: Springer, 1986. [ Links ]

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

Received: April 13, 2017; Accepted: December 14, 2018

*Correspondencia: Bruno Suzuki, Departamento de Matemáticas, Universidad Católica del Norte, Facultad de Ciencias, Av. Angamos 0610, Antofagasta - Chile. Correo electrónico: obrunosuzuki@gmail.com. DOI: https://doi.org/10.15446/recolma.v1n52.74554

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