Landau-Ginzburg Hodge numbers for mirrors of del Pezzo surfaces
Valery Lunts, Victor Przyjalkowski
TL;DR
This paper investigates conjectures relating to Landau-Ginzburg Hodge numbers for mirror pairs of del Pezzo surfaces, verifying some and providing a counterexample in the two-dimensional case.
Contribution
It tests existing conjectures on Landau-Ginzburg Hodge numbers for del Pezzo surface mirrors, confirming some and challenging others with a counterexample.
Findings
Verification of some conjectures in dimension two
Counterexample to certain conjectures in the same setting
Insights into Landau-Ginzburg Hodge number behavior
Abstract
We consider the conjectures from the paper by Katzarkov, Kontsevich, and Pantev about Landau-Ginzburg Hodge numbers associated to tamely compactifiable Landau-Ginzburg models. We test these conjectures in case of dimension two, verifying some and giving a counterexample to the other.
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