Derived categories and rationality of conic bundles

Update: 2011-07-01

Description

In this talk I present a joint work with Marcello Bernardara where we show that a standard conic bundle on a rational minimal surface is rational if and only if its derived category admits a semiothogonal decomposition via derived categories of smooth projective curves and exceptional objects. In particular, even if the surface is not minimal, such a decomposition allows to reconstruct the intermediate Jacobian as the direct sum of the Jacobian of those curves.

Comments

In Channel

Vector bundles and coherent systems on nodal curves

2011-07-2552:28

Higgs bundles and quaternionic geometry

2011-07-0401:05:32

Moduli spaces of locally homogeneous geometric structures

2011-07-0401:04:39

Bridgeland stability conditions and Fourier-Mukai transforms

2011-07-0101:03:12

Deligne-Hodge polynomials for SL(2,C)-character varieties of genus 1 and 2.

2011-07-0129:43

Derived equivalences of Azumaya algebras on K3 surfaces

2011-07-0130:29

Derived categories and rationality of conic bundles

2011-07-0126:56

Stability conditions for the local projective plane

2011-07-0152:06

Kahler-Einstein metrics and Geometric Invariant Theory

2011-07-0101:06:18

Introduction to moduli of varieties - IV: Surfaces of general type related to abelian varieties and hyperplane arrangements

2011-07-0101:05:24

Monopoles on the product of a surface and the circle

2011-06-3001:06:22

Vortices on Riemann Surfaces

2011-06-3001:05:08

Rank two Brill-Noether theory and the birational geometry of the moduli space of curves

2011-06-3001:06:31

Universal plane curve and moduli spaces of 1-dimensional coherent sheaves

2011-06-3026:23

Topology of moduli spaces of vector bundles on a real algebraic curve

2011-06-3031:19

Moduli of plane sheaves supported on curves of low multiplicity

2011-06-2929:10

Brill-Noether theory for vector bundles with fixed determinant

2011-06-2956:03

Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0

2011-06-2959:58

Refined curve counting on algebraic surfaces

2011-06-2901:02:01

Compactifications of reductive groups as moduli stacks of bundles

2011-06-2936:00

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Derived categories and rationality of conic bundles

#box-pro-ellipsis-176242822361690{-webkit-line-clamp:2;}Derived categories and rationality of conic bundles

Derived categories and rationality of conic bundles

Steve Greenham

Derived categories and rationality of conic bundles