Λεπτομέρειες βιβλιογραφικής εγγραφής
| 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: |
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