Homological Geometry and Mirror Symmetry

Alexander B. Givental
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Alexander B. Givental: University of California-Berkeley, Department of Mathematics

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 472-480 from Springer

Abstract: Abstract A homogeneous polynomial equation in five variables determines a quintic 3-fp;d in ℂP4. Hodge numbers of a nonsingular quintic are know to be: h p, p = 1, p = 0, 1, 2, 3 (Kähler form and its powers), h3, 0 = h0,3 = 1 (a quintic happens to bear a holomorphic volume form), h2,1 = h1, 2 = 101 = 126 - 25 (it is the dimension of the space of all quintics modulo projective transformations, and h2,1 is responsible here for infinitesimal variations of the complex structure) and all the other h p,q = 0.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_40

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