In recent years an interesting connection has been established between some moduli spaces of algebro-geometric objects (e.g. algebraic stable curves) and some modulispaces of polyhedral objects (e.g. tropical curves).In loose words, this connection expresses the Berkovich skeleton of a given algebrogeometric moduli space as the moduli space of the skeleta of the objects parametrizedby the given space; it has been proved to hold in two important cases: the modulispace of stable curves and the moduli space of admissible covers. Partial results areknown in other cases.This connection relies on the study of the boundary of the algebro-geometric moduli spaces and on its recursive, combinatorial properties, some of which have beenlong known and are now viewed from a new perspective.

Caporaso, L. (2018). Recursive combinatorial aspects of compactified moduli spaces. In Proceedings of the International Congress of Mathematicians, ICM 2018 (pp.653-670). World Scientific Publishing Co Pte Ltd.

Recursive combinatorial aspects of compactified moduli spaces

Caporaso L.
2018

Abstract

In recent years an interesting connection has been established between some moduli spaces of algebro-geometric objects (e.g. algebraic stable curves) and some modulispaces of polyhedral objects (e.g. tropical curves).In loose words, this connection expresses the Berkovich skeleton of a given algebrogeometric moduli space as the moduli space of the skeleta of the objects parametrizedby the given space; it has been proved to hold in two important cases: the modulispace of stable curves and the moduli space of admissible covers. Partial results areknown in other cases.This connection relies on the study of the boundary of the algebro-geometric moduli spaces and on its recursive, combinatorial properties, some of which have beenlong known and are now viewed from a new perspective.
Caporaso, L. (2018). Recursive combinatorial aspects of compactified moduli spaces. In Proceedings of the International Congress of Mathematicians, ICM 2018 (pp.653-670). World Scientific Publishing Co Pte Ltd.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/374601
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