Asian Journal of Mathematics
- Asian J. Math.
- Volume 18, Number 2 (2014), 345-364.
The Euclid-Fourier-Mukai algorithm for elliptic surfaces
We describe the birational correspondences, induced by the Fourier-Mukai functor, between moduli spaces of semistable sheaves on elliptic surfaces with sections, using the notion of $P$-stability in the derived category. We give explicit conditions to determine whether these correspondences are isomorphisms. This is indeed not true in general and we describe the cases where the birational maps are Mukai flops. Moreover, this construction provides examples of new compactifications of the moduli spaces of vector bundles via sheaves with torsion and via complexes. We finally get for any fixed dimension an isomorphism between the Picard groups of the moduli spaces.
Asian J. Math., Volume 18, Number 2 (2014), 345-364.
First available in Project Euclid: 27 August 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14J27: Elliptic surfaces 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Bernardara, Marcello; Hein, Georg. The Euclid-Fourier-Mukai algorithm for elliptic surfaces. Asian J. Math. 18 (2014), no. 2, 345--364. https://projecteuclid.org/euclid.ajm/1409168528