By Kimura & Vaintrob Jarvis
This quantity is a set of articles on orbifolds, algebraic curves with greater spin buildings, and similar invariants of Gromov-Witten style. Orbifold Gromov-Witten thought generalizes quantum cohomology for orbifolds, while spin cohomological box concept relies at the moduli areas of upper spin curves and is said by way of Witten's conjecture to the Gelfand-Dickey integrable hierarchies. a typical characteristic of those very diversified taking a look theories is the critical function performed via orbicurves in either one of them. Insights in a single idea can usually yield insights into the opposite. This ebook brings jointly for the 1st time papers relating to either side of this interplay. The articles within the assortment conceal varied subject matters, resembling geometry and topology of orbifolds, cohomological box theories, orbifold Gromov-Witten concept, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of upper spin curves and spin cohomological box idea
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Additional info for Gromov-Witten Theory of Spin Curves and Orbifolds: AMS Special Session on Gromov-Witten Theory of Spin Curves and Orbifolds, May 3-4, 2003, San Franci
This is a straightforward generalization in the case of curves of the one given by Mumford in . A. Barja and L. Stoppino Let C be a smooth curve, and let 'W C ! Pr 1 be a non-degenerate morphism. C; L / of dimension r such that ' is induced from the linear series jV j. e. jV j is a gdr 1 on C ). Linear stability gives a lower bound on the slope between the degree and the dimension of any projections, depending on the degree and dimension of the given linear series as follows. Definition 6. C; V /, is linearly semistable (resp.
RP 1/ for i D 1; : : : ; l (dlC1 D dl ) and that ri C1 i Observe that degG D li D1 ri . i i C1 / to get L2 2adegG a. 1 C ri C 1. l /; which finally proves 2adl d degG D 2 degG : a C dl r L2 Remark 23. The fact that we used Clifford’s theorem in the proof of the slope inequality via Xiao’s method in Example 3 can thus be rephrased in the following way: Clifford’s theorem implies the linear semistability of the general fibres of f together with their canonical systems. We can make the following improvement for the complete case.
Reine Angew. Math. 480, 177–195 (1996) 40. I. Morrison, Projective stability of ruled surfaces. Invent. Math. 56(3), 269–304 (1980) 41. I. Morrison, Stability of Hilbert Points of Generic K3 Surfaces, vol. 401 (Centre de Recerca Matemática, Bellaterra, 1999) 42. D. Mumford, Stability of projective varieties. L’Ens. Math. 23, 39–110 (1977) 43. D. Mumford, J. Fogarty, F. Kirwan, Geometric Invariant Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 34(2), 3rd edn. (Springer, Berlin, 1994) 44.
Gromov-Witten Theory of Spin Curves and Orbifolds: AMS Special Session on Gromov-Witten Theory of Spin Curves and Orbifolds, May 3-4, 2003, San Franci by Kimura & Vaintrob Jarvis
Categories: Algebraic Geometry