An overview on curve semistable and numerically flat Higgs bundles

Capasso, Armando

doi:10.15517/0crtrw10

Autores/as

Armando Capasso Università degli Studi di Trieste, Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche “Bruno de Finetti”, Trieste, Italy. Autor/a

DOI:

https://doi.org/10.15517/0crtrw10

Palabras clave:

Fibrados de Higgs, Semiestabilidad de curvas, Numéricamente plano, Nociones de positividad

Resumen

Después de recordar las nociones básicas sobre los esquemas de Higgs-Grassmann, examinamos cómo se puede utilizar estas para definir generalizaciones de nociones de positividad, como la planitud numérica, que “detectan” el campo de Higgs. Luego demostramos varias propiedades de fibrados de Higgs sobre variedad proyectivas suaves definidas sobre campos algebraicamentes cerrados de característica 0, que satisfacen estas condiciones. Por último, analizamos cómo se pueden conectar estos con los llamados fibrados de Higgs semiestables en las curvas.

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