Deformations of Zappatic surfaces and their Galois covers

Meirav Amram; Cheng Gong; Jia Li Mo; János Kollár

doi:10.1016/j.jalgebra.2026.01.015

Deformations of Zappatic surfaces and their Galois covers

Meirav Amram
, Cheng Gong
, Jia Li Mo
, János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper considers some algebraic surfaces that can deform to planar Zappatic surfaces with a unique singularity of type E_n. We prove that the Galois covers of these surfaces are all simply connected of general type, for n≥4. We also give a formula for a local Zappatic singularity of a Zappatic surface of type E_n. As an application, we prove that such surfaces do not exist for n>30. Furthermore, Kollár improves the result to n>9 in Appendix A.

Original language	English (US)
Pages (from-to)	710-731
Number of pages	22
Journal	Journal of Algebra
Volume	693
DOIs	https://doi.org/10.1016/j.jalgebra.2026.01.015
State	Published - May 1 2026

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Deformation
Fundamental group
Galois cover
Zappatic surface

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10.1016/j.jalgebra.2026.01.015

Cite this

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title = "Deformations of Zappatic surfaces and their Galois covers",

abstract = "This paper considers some algebraic surfaces that can deform to planar Zappatic surfaces with a unique singularity of type En. We prove that the Galois covers of these surfaces are all simply connected of general type, for n≥4. We also give a formula for a local Zappatic singularity of a Zappatic surface of type En. As an application, we prove that such surfaces do not exist for n>30. Furthermore, Koll{\'a}r improves the result to n>9 in Appendix A.",

keywords = "Deformation, Fundamental group, Galois cover, Zappatic surface",

author = "Meirav Amram and Cheng Gong and Mo, \{Jia Li\} and J{\'a}nos Koll{\'a}r",

note = "Publisher Copyright: {\textcopyright} 2026",

year = "2026",

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day = "1",

doi = "10.1016/j.jalgebra.2026.01.015",

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T1 - Deformations of Zappatic surfaces and their Galois covers

AU - Amram, Meirav

AU - Gong, Cheng

AU - Mo, Jia Li

AU - Kollár, János

PY - 2026/5/1

Y1 - 2026/5/1

N2 - This paper considers some algebraic surfaces that can deform to planar Zappatic surfaces with a unique singularity of type En. We prove that the Galois covers of these surfaces are all simply connected of general type, for n≥4. We also give a formula for a local Zappatic singularity of a Zappatic surface of type En. As an application, we prove that such surfaces do not exist for n>30. Furthermore, Kollár improves the result to n>9 in Appendix A.

AB - This paper considers some algebraic surfaces that can deform to planar Zappatic surfaces with a unique singularity of type En. We prove that the Galois covers of these surfaces are all simply connected of general type, for n≥4. We also give a formula for a local Zappatic singularity of a Zappatic surface of type En. As an application, we prove that such surfaces do not exist for n>30. Furthermore, Kollár improves the result to n>9 in Appendix A.

KW - Deformation

KW - Fundamental group

KW - Galois cover

KW - Zappatic surface

UR - https://www.scopus.com/pages/publications/105028446967

UR - https://www.scopus.com/pages/publications/105028446967#tab=citedBy

U2 - 10.1016/j.jalgebra.2026.01.015

DO - 10.1016/j.jalgebra.2026.01.015

M3 - Article

AN - SCOPUS:105028446967

SN - 0021-8693

VL - 693

SP - 710

EP - 731

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Deformations of Zappatic surfaces and their Galois covers

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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