Deformations of product-quotient surfaces and reconstruction of Todorov surfaces via $\mathbb{Q}$-Gorenstein smoothing
| Autor: | Francesco Polizzi, Yongnam Lee |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
14J10 Group (mathematics) Surface of general type Deformation (meteorology) Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry $\mathbb{Q}$-Gorenstein smoothing Genus (mathematics) Product (mathematics) FOS: Mathematics 14J29 14J29 (Primary) 14J10 14J17 (Secondary) 14J17 Algebraic Geometry (math.AG) product-quotient surface Quotient Smoothing Mathematics |
| Zdroj: | Algebraic Geometry in East Asia — Taipei 2011, J. A. Chen, M. Chen, Y. Kawamata and J. Keum, eds. (Tokyo: Mathematical Society of Japan, 2015) |
| DOI: | 10.48550/arxiv.1201.4925 |
| Popis: | We consider the deformation spaces of some singular product-quotient surfaces $X=(C_1 \times C_2)/G$, where the curves $C_i$ have genus 3 and the group $G$ is isomorphic to $\mathbb{Z}_4$. As a by-product, we give a new construction of Todorov surfaces with $p_g=1$, $q=0$ and $2\le K^2\le 8$ by using $\mathbb{Q}$-Gorenstein smoothings. Comment: 21 pages, Minor changes are made. It will apper in Advanced Studies in Pure Mathematics (Proceeding of Algebraic Geometry in East Asia, Taipei) |
| Databáze: | OpenAIRE |
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