التفاصيل البيبلوغرافية
| العنوان: |
Surfaces of General Type with Maximal Picard Number Near the Noether Line. |
| المؤلفون: |
Bin, Nguyen, Lorenzo, Vicente |
| المصدر: |
IMRN: International Mathematics Research Notices; Jun2024, Vol. 2024 Issue 12, p9792-9807, 16p |
| مصطلحات موضوعية: |
PICARD number, ALGEBRAIC surfaces |
| مستخلص: |
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 also provide infinitely many new examples of algebraic surfaces of general type with maximal Picard number above the Noether line. [ABSTRACT FROM AUTHOR] |
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