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Search: MSC category 14J29 ( Surfaces of general type )

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1. CJM Online first

Wang, Zhenjian
On algebraic surfaces associated with line arrangements
For a line arrangement $\mathcal{A}$ in the complex projective plane $\mathbb{P}^2$, we investigate the compactification $\overline{F}$ in $\mathbb{P}^3$ of the affine Milnor fiber $F$ and its minimal resolution $\widetilde{F}$. We compute the Chern numbers of $\widetilde{F}$ in terms of the combinatorics of the line arrangement $\mathcal{A}$. As applications of the computation of the Chern numbers, we show that the minimal resolution is never a quotient of a ball; in addition, we also prove that $\widetilde{F}$ is of general type when the arrangement has only nodes or triple points as singularities; finally, we compute all the Hodge numbers of some $\widetilde{F}$ by using some knowledge about the Milnor fiber monodromy of the arrangement.

Keywords:line arrangement, Milnor fiber, algebraic surface, Chern number
Categories:32S22, 32S25, 14J17, 14J29, 14J70

2. CJM 2015 (vol 68 pp. 67)

Ishida, Hirotaka
A Lower Bound on the Euler-Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves
Let $S$ be a surface of general type. In this article, when there exists a relatively minimal hyperelliptic fibration $f \colon S \rightarrow \mathbb{P}^1$ whose slope is less than or equal to four, we show the lower bound on the Euler-Poincaré characteristic of $S$. Furthermore, we prove that our bound is the best possible by giving required hyperelliptic fibrations.

Keywords:hyperelliptic fibration, surface of general type, double cover
Categories:14D05, 14J29, 14H30

3. CJM 2012 (vol 65 pp. 195)

Penegini, Matteo; Polizzi, Francesco
Surfaces with $p_g=q=2$, $K^2=6$, and Albanese Map of Degree $2$
We classify minimal surfaces of general type with $p_g=q=2$ and $K^2=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth irreducible components $\mathcal{M}_{Ia}$, $\mathcal{M}_{Ib}$, $\mathcal{M}_{II}$ of dimension $4$, $4$, $3$, respectively.

Keywords:surface of general type, abelian surface, Albanese map
Categories:14J29, 14J10

4. CJM 2005 (vol 57 pp. 724)

Purnaprajna, B. P.
Some Results on Surfaces of General Type
In this article we prove some new results on projective normality, normal presentation and higher syzygies for surfaces of general type, not necessarily smooth, embedded by adjoint linear series. Some of the corollaries of more general results include: results on property $N_p$ associated to $K_S \otimes B^{\otimes n}$ where $B$ is base-point free and ample divisor with $B\otimes K^*$ {\it nef}, results for pluricanonical linear systems and results giving effective bounds for adjoint linear series associated to ample bundles. Examples in the last section show that the results are optimal.

Categories:13D02, 14C20, 14J29

5. CJM 2003 (vol 55 pp. 649)

Zucconi, Francesco
Surfaces with $p_{g}=q=2$ and an Irrational Pencil
We describe the irrational pencils on surfaces of general type with $p_{g}=q=2$.

Categories:14J29, 14J25, 14D06, 14D99

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