Algebraic Geometry: Seattle 2005, Summer Research Institute by D. Abramovich, A. Bertram, L. Katzarkov, R. Pandharipande,

By D. Abramovich, A. Bertram, L. Katzarkov, R. Pandharipande, M. Thaddeus (ed.)

The 2005 AMS summer season Institute on Algebraic Geometry in Seattle used to be a major occasion. With over 500 contributors, together with the various world's top specialists, it used to be possibly the biggest convention on algebraic geometry ever held. those court cases volumes current learn and expository papers by means of one of the most striking audio system on the assembly, vividly conveying the grandeur and energy of the topic. the main fascinating themes in present algebraic geometry study obtain very plentiful remedy. for example, there's enlightening details on some of the most recent technical instruments, from jet schemes and derived different types to algebraic stacks. various papers delve into the geometry of assorted moduli areas, together with these of solid curves, sturdy maps, coherent sheaves, and abelian kinds. different papers talk about the hot dramatic advances in higher-dimensional bi rational geometry, whereas nonetheless others hint the impression of quantum box thought on algebraic geometry through replicate symmetry, Gromov - Witten invariants, and symplectic geometry. The court cases of prior algebraic geometry AMS Institutes, held at Woods gap, Arcata, Bowdoin, and Santa Cruz, became classics. the current volumes promise to be both influential. They current the cutting-edge in algebraic geometry in papers that might have extensive curiosity and enduring price

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Extra info for Algebraic Geometry: Seattle 2005, Summer Research Institute July 25-August 12, 2005, University of Washington, Seattle, Washington part 2

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46] A. AG/0506347. [47] R. Thomas, Moment maps, monodromy and mirror manifolds. In Symplectic geometry and mirror symmetry, eds K. -G. Oh, K. Ono and G. Tian. World Scientific, 2001, 467-498. [48] R. Thomas, Stability conditions and the braid group, Comm. Anal. Geom. 14 (2006), no. 1, 135–161. [49] Y. AG/0512648. [50] Y. AG/0608495. [51] A. Veselov, On geometry of a special class of solutions to generalized WDVV equations, Integrability: the Seiberg-Witten and Whitham equations (Edinburgh, 1998), 125–135, Gordon and Breach, Amsterdam, 2000.

A } for Horb (X ) and we define the potential function for X: F X (x0 , . . , xa , u1 , . . ,na =0 β X β xn0 0 xna · · · a ud11 · · · uds s n0 ! na ! where β = d1 π∗ β1 + · · · + ds π∗ βs is summed over all s-tuple (d1 , . . , ds ) of nonnegative integers. The inertia stack IX of an orbifold X is defined to be the fibered product of X with itself over the diagonal in X ×X . The points of IX are pairs (x, g) where x ∈ X and g ∈ AutX (x). There is an involution I of IX taking (x, g) to (x, g −1 ).

2 Since the only remaining non-vanishing invariants are then Dn we actually need only consider the connected component of M 0,n (BZ2 ) where all the evaluation ord maps go to the twisted sector. Setting n = 2g + 2, we denote this space as H g . Concretely, it is the usual compactified moduli space of hyperelliptic curves (with ord ordered branch points). The virtual class on H g is given by e(R1 π∗ f ∗ (L ⊕ L)) where f and π are the universal map and universal curve for M 0,n (BZ2 ) and L ⊕ L → BZ2 is two copies of the non-trivial line bundle over BZ2 with the torus acting with weight t1 on the first factor and with weight t2 on the second factor.

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