爆炸和表面的量子光谱

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-07-10 DOI:10.1016/j.aim.2025.110432

Ádám Gyenge , Szilárd Szabó

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引用次数: 0

摘要

我们研究了在爆炸作用下光滑射影表面的量子（或杜布罗文）连接谱的行为。我们的主要结果是，对于参数的小值，这样一个表面的量子谱是表面的最小模型的量子谱和位于“接近无穷”的有限数量的附加点的渐近联合，这些附加点客观地对应于例外除数。这证明了Kontsevich在表面情况下的一个猜想。

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Blow-ups and the quantum spectrum of surfaces

We investigate the behavior of the spectrum of the quantum (or Dubrovin) connection of smooth projective surfaces under blow-ups. Our main result is that for small values of the parameters, the quantum spectrum of such a surface is asymptotically the union of the quantum spectrum of a minimal model of the surface and a finite number of additional points located “close to infinity”, that correspond bijectively to the exceptional divisors. This proves a conjecture of Kontsevich in the surface case.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.