scholarly journals The Albanese map of a 3-fold of general type whose canonical map is composed with a pencil

2002 ◽  
Vol 240 (3) ◽  
pp. 511-519
Author(s):  
Jin-Xing Cai
Keyword(s):  
General Type ◽  
Canonical Map ◽  
Albanese Map

scholarly journals Cuspidal quintics and surfaces with , and 5-torsion

2016 ◽  
Vol 19 (1) ◽  
pp. 42-53
Author(s):  
Carlos Rito
Keyword(s):  
Computer Algebra ◽  
General Type ◽  
Free Action ◽  
The Other ◽  
Singular Set ◽  
Canonical Map ◽  
Singular Sets ◽  
Surface Of General Type ◽  
Quintic Threefold ◽  
Hyperplane Sections

If $S$ is a quintic surface in $\mathbb{P}^{3}$ with singular set 15 3-divisible ordinary cusps, then there is a Galois triple cover ${\it\phi}:X\rightarrow S$ branched only at the cusps such that $p_{g}(X)=4$, $q(X)=0$, $K_{X}^{2}=15$ and ${\it\phi}$ is the canonical map of $X$. We use computer algebra to search for such quintics having a free action of $\mathbb{Z}_{5}$, so that $X/\mathbb{Z}_{5}$ is a smooth minimal surface of general type with $p_{g}=0$ and $K^{2}=3$. We find two different quintics, one of which is the van der Geer–Zagier quintic; the other is new.We also construct a quintic threefold passing through the 15 singular lines of the Igusa quartic, with 15 cuspidal lines there. By taking tangent hyperplane sections, we compute quintic surfaces with singular sets $17\mathsf{A}_{2}$, $16\mathsf{A}_{2}$, $15\mathsf{A}_{2}+\mathsf{A}_{3}$ and $15\mathsf{A}_{2}+\mathsf{D}_{4}$.

scholarly journals A note on a family of surfaces with $$p_g=q=2$$ and $$K^2=7$$

2021 ◽  
Author(s):  
Matteo Penegini ◽  
Roberto Pignatelli
Keyword(s):  
Open Subset ◽  
Moduli Space ◽  
General Type ◽  
Connected Components ◽  
Surfaces Of General Type ◽  
Alternative Construction ◽  
Albanese Map

AbstractWe study a family of surfaces of general type with $$p_g=q=2$$ p g = q = 2 and $$K^2=7$$ K 2 = 7 , originally constructed by C. Rito in [35]. We provide an alternative construction of these surfaces, that allows us to describe their Albanese map and the corresponding locus $$\mathcal {M}$$ M in the moduli space of surfaces of general type. In particular we prove that $$\mathcal {M}$$ M is an open subset, and it has three connected components, all of which are 2-dimensional, irreducible and generically smooth

scholarly journals Surfaces with pg = q = 2, K2 = 6, and Albanese Map of Degree 2

2013 ◽  
Vol 65 (1) ◽  
pp. 195-221 ◽  
Author(s):  
Matteo Penegini ◽  
Francesco Polizzi
Keyword(s):  
Moduli Space ◽  
Minimal Surfaces ◽  
General Type ◽  
Disjoint Union ◽  
Double Cover ◽  
Surfaces Of General Type ◽  
Irreducible Components ◽  
Albanese Map

AbstractWe classify minimal surfaces of general type with pg = q = 2 and K2 = 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 MIa, MIb, MII of dimension 4, 4, 3, respectively.

scholarly journals Some infinite sequences of canonical covers of degree 2

2021 ◽  
Vol 21 (1) ◽  
pp. 143-148
Author(s):  
Nguyen Bin
Keyword(s):  
General Type ◽  
Canonical System ◽  
Surfaces Of General Type ◽  
Canonical Map ◽  
Base Points ◽  
Surface Of General Type ◽  
Infinite Sequences

Abstract In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.

scholarly journals On 6-canonical map of irregular threefolds of general type

2013 ◽  
Vol 20 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Jungkai Chen ◽  
Meng Chen ◽  
Zhi Jiang
Keyword(s):  
General Type ◽  
Canonical Map

scholarly journals A Family of Threefolds of General Type with Canonical Map of High Degree

2020 ◽  
Vol 24 (5) ◽  
pp. 1107-1115
Author(s):  
Davide Frapporti ◽  
Christian Gleissner
Keyword(s):  
General Type ◽  
Canonical Map ◽  
High Degree

scholarly journals CANONICALLY FIBERED SURFACES OF GENERAL TYPE

2018 ◽  
Vol 19 (1) ◽  
pp. 209-229
Author(s):  
Xin Lü
Keyword(s):  
General Type ◽  
Complex Surface ◽  
The Other ◽  
Complex Surfaces ◽  
Surfaces Of General Type ◽  
Geometric Genus ◽  
Canonical Map ◽  
Other Hand ◽  
Surface Of General Type

In this paper, we construct the first examples of complex surfaces of general type with arbitrarily large geometric genus whose canonical maps induce non-hyperelliptic fibrations of genus $g=4$, and on the other hand, we prove that there is no complex surface of general type whose canonical map induces a hyperelliptic fibrations of genus $g\geqslant 4$ if the geometric genus is large.

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