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On Combinatorial Bounds for the Total Tjurina Numbers of Certain Curves and Surfaces With Isolated Singularities.

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Τίτλος: On Combinatorial Bounds for the Total Tjurina Numbers of Certain Curves and Surfaces With Isolated Singularities.
Συγγραφείς: Pokora, Piotr1 (AUTHOR) piotr.pokora@uken.krakow.pl
Πηγή: Mathematische Nachrichten. Oct2026, Vol. 299 Issue 10, p2751-2759. 9p.
Θεματικοί όροι: *Conic sections, *Mathematical singularities, *Mathematical bounds, *Hypersurfaces, *Combinatorial optimization
Περίληψη: We investigate combinatorial bounds for the total Tjurina numbers of some plane curve arrangements. Focusing on arrangements of lines and conics in P2$\mathbb {P}^2$ that admit only ordinary quasi‐homogeneous singularities, we derive new structural inequalities governing the distribution of multiple intersection points. As a consequence, we establish sharp lower bounds for the total Tjurina numbers of free line arrangements with bounded maximal multiplicity and, more generally, for free conic‐line arrangements. In particular, we show that for a free arrangement of d$d$ lines and k$k$ conics, the total Tjurina number grows at least quadratically in d$d$ and k$k$, and we demonstrate that this bound is sharp. As an application of these planar results, we construct a special family of surfaces in P3$\mathbb {P}^{3}$ with only isolated singularities and arbitrarily large total Tjurina numbers. This provides new lower bounds for the total Tjurina numbers of certain hypersurfaces that are independent of detailed homological data. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
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Header DbId: asx
DbLabel: Academic Search Index
An: 197591281
RelevancyScore: 1452
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 1452.43029785156
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  Label: Title
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  Data: On Combinatorial Bounds for the Total Tjurina Numbers of Certain Curves and Surfaces With Isolated Singularities.
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  Data: <searchLink fieldCode="AR" term="%22Pokora%2C+Piotr%22">Pokora, Piotr</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> piotr.pokora@uken.krakow.pl</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematische+Nachrichten%22">Mathematische Nachrichten</searchLink>. Oct2026, Vol. 299 Issue 10, p2751-2759. 9p.
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  Data: *<searchLink fieldCode="DE" term="%22Conic+sections%22">Conic sections</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+bounds%22">Mathematical bounds</searchLink><br />*<searchLink fieldCode="DE" term="%22Hypersurfaces%22">Hypersurfaces</searchLink><br />*<searchLink fieldCode="DE" term="%22Combinatorial+optimization%22">Combinatorial optimization</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We investigate combinatorial bounds for the total Tjurina numbers of some plane curve arrangements. Focusing on arrangements of lines and conics in P2$\mathbb {P}^2$ that admit only ordinary quasi‐homogeneous singularities, we derive new structural inequalities governing the distribution of multiple intersection points. As a consequence, we establish sharp lower bounds for the total Tjurina numbers of free line arrangements with bounded maximal multiplicity and, more generally, for free conic‐line arrangements. In particular, we show that for a free arrangement of d$d$ lines and k$k$ conics, the total Tjurina number grows at least quadratically in d$d$ and k$k$, and we demonstrate that this bound is sharp. As an application of these planar results, we construct a special family of surfaces in P3$\mathbb {P}^{3}$ with only isolated singularities and arbitrarily large total Tjurina numbers. This provides new lower bounds for the total Tjurina numbers of certain hypersurfaces that are independent of detailed homological data. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1002/mana.70217
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 9
        StartPage: 2751
    Subjects:
      – SubjectFull: Conic sections
        Type: general
      – SubjectFull: Mathematical singularities
        Type: general
      – SubjectFull: Mathematical bounds
        Type: general
      – SubjectFull: Hypersurfaces
        Type: general
      – SubjectFull: Combinatorial optimization
        Type: general
    Titles:
      – TitleFull: On Combinatorial Bounds for the Total Tjurina Numbers of Certain Curves and Surfaces With Isolated Singularities.
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            NameFull: Pokora, Piotr
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          Dates:
            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
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              Value: 0025584X
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              Value: 299
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              Value: 10
          Titles:
            – TitleFull: Mathematische Nachrichten
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