Algebraic Geometry and Topological Strings Seminar  RSS

Sessions

03/11/2005, 18:00 — 19:00 — Amphitheatre Pa3, Mathematics Building
Victor Przyjalkowski, Mathematical Institute of Russian Academy of Science, Moscow

Generalized Givental's Theorem and classification of Fano threefolds

We present Golyshev's modularity conjecture that states that the counting equations for Fano threefolds with Picard group Z (which codes their Gromov-Witten invariants) are modular. To check it we find Gromov-Witten infariants of them. For this we generalise Givental's Theorem (in the Fano case) that gives us Gromov-Witten invariants for complete intersections in toric varieties with non-negative canonical bundle.

REFERENCES:
  • V. Golyshev, The geometricity problem and modularity of some Riemann-Roch variations, Dokl. Akad. Nauk 386 (2002) 583-588.
  • V. Przyjalkowski, Quantum cohomology of smooth complete intersections in weighted projective spaces and singular toric varieties, math.AG/0507232.
  • A. Givental, A mirror theorem for toric complete intersections, Topological field theory, primitive forms and related topics (Kyoto, 1996), 141-175, alg-geom/9701016

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