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 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 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 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.

The canonical volume of minimal 3-folds of general type

2018 ◽  
Vol 29 (03) ◽  
pp. 1850023
Author(s):  
Huanping Zhu
Keyword(s):  
Linear System ◽  
Lower Bounds ◽  
General Type ◽  
Rational Map ◽  
Canonical Map ◽  
Volume Formula ◽  
Complete Linear System ◽  
Minimal Formula

Let [Formula: see text] be a nonsingular projective [Formula: see text]-fold of general type. Denote by [Formula: see text] the [Formula: see text]-canonical map of [Formula: see text] which is the rational map naturally associated to the complete linear system [Formula: see text]. Suppose that [Formula: see text] be a minimal [Formula: see text]-fold of [Formula: see text] and [Formula: see text] the pluricanonical section index. In this paper, we obtain the lower bounds of the canonical volume [Formula: see text] in term of [Formula: see text] for [Formula: see text]. In addition, we also classify the weighted baskets [Formula: see text] of [Formula: see text] satisfying [Formula: see text].

scholarly journals Irregular Canonical Double Surfaces

1998 ◽  
Vol 152 ◽  
pp. 203-230 ◽  
Author(s):  
Margarida Mendes Lopes ◽  
Rita Pardini
Keyword(s):  
General Type ◽  
Surfaces Of General Type ◽  
Irregular Surfaces ◽  
Canonical Map

Abstract.We classify minimal irregular surfaces of general type X with Kx ample and such that the canonical map is 2-to-l onto a canonically embedded surface.

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