Publication

MODULI OF Q-GORENSTEIN PAIRS AND APPLICATIONS

Stefano Filipazzi
2024
Journal Articles

Abstract

We develop a framework to construct moduli spaces of Q-Gorenstein pairs. To do so, we fix certain invariants; these choices are encoded in the notion of Q-stable pair. We show that these choices give a proper moduli space with projective coarse moduli space and they prevent some pathologies of the moduli space of stable pairs when the coefficients are smaller than 21. Lastly, we apply this machinery to provide an alternative proof of the projectivity of the moduli space of stable pairs.

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https://infoscience.epfl.ch/entities/publication/dc59df2c-c1ec-41a8-82a8-0015b413d651

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Stefano Filipazzi
2024
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/dc59df2c-c1ec-41a8-82a8-0015b413d651

About this result

Related concepts (9)

Moduli space

In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space.

Moduli of algebraic curves

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on the restrictions applied to the classes of algebraic curves considered, the corresponding moduli problem and the moduli space is different. One also distinguishes between fine and coarse moduli spaces for the same moduli problem.

Moduli stack of elliptic curves

In mathematics, the moduli stack of elliptic curves, denoted as or , is an algebraic stack over classifying elliptic curves. Note that it is a special case of the moduli stack of algebraic curves . In particular its points with values in some field correspond to elliptic curves over the field, and more generally morphisms from a scheme to it correspond to elliptic curves over . The construction of this space spans over a century because of the various generalizations of elliptic curves as the field has developed.

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