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Nguyen Bin

Publications and source records attributed to Nguyen Bin.

11 recordsLinked to original sources
arXiv2024

Infinitely many new sequences of surfaces of general type with maximal Picard number converging to the Severi line

Examples of algebraic surfaces of general type with maximal Picard number are not abundant in the literature. Moreover, most known examples either possess low invariants, lie near the Noether line $K^2=2\chi-6$ or are somewhat scattered. A notable exception is Persson's sequence of double covers of the projective plane with maximal Picard number, whose invariants converge to the Severi line $K^2=4\chi$. This note is devoted to the construction of infinitely many new sequences of surfaces of general type with maximal Picard number whose invariants converge to the Severi line.

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arXiv2024

Log canonical thresholds of Burniat surfaces with $K^2 = 5$

In the paper we compute the global log canonical thresholds of the secondary Burniat surfaces with $K^2 = 5$. Furthermore, we establish optimal lower bounds for the log canonical thresholds of members in pluricanonical sublinear systems of the secondary Burniat surfaces with $K^2 = 5$.

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arXiv2023

Surfaces of general type with maximal Picard number near the Noether line

The first published non-trivial examples of algebraic surfaces of general type with maximal Picard number are due to Persson, who constructed surfaces with maximal Picard number on the Noether line $K^2=2\chi-6$ for every admissible pair $(K^2,\chi)$ such that $\chi \not\equiv 0 \text{ mod } 6$. In this note, given a non-negative integer $k$, algebraic surfaces of general type with maximal Picard number lying on the line $K^2=2\chi-6+k$ are constructed for every admissible pair $(K^2,\chi)$ such that $\chi\geq 2k+10$. These constructions, obtained as bidouble covers of rational surfaces, not only allow to fill in Persson's gap on the Noether line, but they provide infinitely many new examples of algebraic surfaces of general type with maximal Picard number above the Noether line.

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arXiv2022

Some algebraic surfaces with canonical map of degree 10, 12, 14

Surfaces of general type with canonical map of degree d bigger than 8 have bounded geometric genus and irregularity. In particular the irregularity is at most 2 if d>= 10. In the present paper, the existence of surfaces with d=10 and all possible irregularities, surfaces with d = 12 and irregularity 1 and 2, and surfaces with d = 14 and irregularity 0 and 1 is proven, by constructing these surfaces as $ \mathbb{Z}_2^3 $-covers of certain rational surfaces. These results together with the construction by C. Rito of a surface with d=12 and irregularity 0 show that all the possibilities for the irregularity in the cases d=10, d=12 can occur, whilst the existence of a surface with d=14 and irregularity 2 is still an open problem.

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arXiv2021

Some examples of algebraic surfaces with canonical map of degree 20

In this note, we construct two minimal surfaces of general type with geometric genus p_g= 3, irregularity q = 0, self-intersection of the canonical divisor K^22 =20,24 such that their canonical map is of degree 20. In one of these surfaces, the canonical linear system has a non-trivial fixed part. These surfaces, to our knowledge, are the first examples of minimal surfaces of general type with canonical map of degree 20.

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arXiv2019

New examples of canonical covers of degree 3

This paper presents new examples of projective surfaces of general type over $\mathbb{C}$ with canonical map of degree $ 3 $ onto a surface of general type. Very few examples are known of such surfaces and some of the examples in this paper present the new feature of having the canonical map not a morphism (i.e. the canonical linear system with base points).

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