Stability and semi-stability of (2,2)-type surfaces

A. J. Parameswaran; Nabanita Ray

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arXiv · 2009.06232

Stability and semi-stability of (2,2)-type surfaces

A. J. Parameswaran·Nabanita Ray

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Abstract

We describe the GIT compactification of the moduli of (2,2)-type effective divisors of $\mathbb{P}^1\times\mathbb{P}^2$ (i.e., surfaces of the linear system $\vert \pi_1^*\mathcal{O}_{\mathbb{P}^1}(2)\otimes \pi_2^*\mathcal{O}_{\mathbb{P}^2}(2)\vert$ ) which are generically Del Pezzo surfaces of degree two. In order to get the compactification, we characterize stable and semi-stable (2,2)-type surfaces, and also determine the equivalence classes of strictly semi-stable (2,2)-type surfaces. Moreover, we describe the boundary of the moduli of (2,2)-type surfaces.

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BibTeX RIS

A. J. Parameswaran, Nabanita Ray. 2020-09-14. Stability and semi-stability of (2,2)-type surfaces. https://arxiv.org/abs/2009.06232

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