The conifold point

Sergey Galkin

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arXiv · 1404.7388

The conifold point

Sergey Galkin

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Abstract

Consider a Laurent polynomial with real positive coefficients such that the origin is strictly inside its Newton polytope. Then it is strongly convex as a function of real positive argument. So it has a distinguished Morse critical point --- the unique critical point with real positive coordinates. As a consequence we obtain a positive answer to a question of Ostrover and Tyomkin: the quantum cohomology algebra of a toric Fano manifold contains a field as a direct summand. Moreover, it gives a good evidence that the same statement holds for any Fano manifold.

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Sergey Galkin. 2014-04-29. The conifold point. https://arxiv.org/abs/1404.7388

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