B. Andreas, = 1 heterotic compactifications, Journal of High Energy Physics, vol.1999, issue.01, p.pp. (electronic), 1999.
DOI : 10.1088/1126-6708/1999/01/011

B. Andreas and G. Curio, Three-branes and five-branes in N=1 dual string pairs, Physics Letters B, vol.417, issue.1-2, pp.41-44, 1998.
DOI : 10.1016/S0370-2693(97)01342-7

B. Andreas and G. Curio, On discrete twist and four-flux in $N = 1$ heterotic/$F$-theory compactifications, Advances in Theoretical and Mathematical Physics, vol.3, issue.5, pp.1325-1413, 1999.
DOI : 10.4310/ATMP.1999.v3.n5.a4

B. Andreas and G. Curio, Horizontal and vertical five-branes in heterotic/F-theory duality, Journal of High Energy Physics, vol.2000, issue.01, p.20, 2000.
DOI : 10.1088/1126-6708/2000/01/013

B. Andreas, H. Ruipérez, and D. , U (n) vector bundles on Calabi-Yau threefolds for string theory compactifications. hep-th, 410170.

B. Andreas, H. Ruipérez, and D. , Comments on <i>N</i> = 1 Heterotic String Vacua, Advances in Theoretical and Mathematical Physics, vol.7, issue.5, pp.751-786, 2003.
DOI : 10.4310/ATMP.2003.v7.n5.a1
URL : http://arxiv.org/abs/hep-th/0305123

B. Andreas, S. Yau, G. Curio, H. Ruipérez, and D. , Fourier-mukai transform and mirror symmetry for D-branes on elliptic Calabi-Yau. math, p.12196

P. S. Aspinwall, A point's point of view of stringy geometry, Journal of High Energy Physics, vol.1997, issue.01, pp.2-15, 2003.
DOI : 10.1016/0550-3213(94)90379-4

P. S. Aspinwall and R. Y. Donagi, The heterotic string, the tangent bundle and derived categories, Advances in Theoretical and Mathematical Physics, vol.2, issue.5, pp.1041-1074, 1998.
DOI : 10.4310/ATMP.1998.v2.n5.a4

P. S. Aspinwall and M. R. Douglas, D-brane stability and monodromy, Journal of High Energy Physics, vol.2000, issue.05, pp.31-35, 2002.
DOI : 10.1016/0550-3213(95)00287-3
URL : http://arxiv.org/abs/hep-th/0110071

P. S. Aspinwall, B. R. Greene, and D. R. Morrison, Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory, Nuclear Physics B, vol.416, issue.2, pp.414-480, 1994.
DOI : 10.1016/0550-3213(94)90321-2

P. S. Aspinwall and D. R. Morrison, Point-like instantons on K3 orbifolds, Nuclear Physics B, vol.503, issue.3, pp.533-564, 1997.
DOI : 10.1016/S0550-3213(97)00516-6
URL : http://doi.org/10.1016/s0550-3213(97)00516-6

M. F. Atiyah, Vector Bundles Over an Elliptic Curve, Proc. London Math. Soc, pp.414-452, 1957.
DOI : 10.1112/plms/s3-7.1.414

C. Bartocci, U. Bruzzo, H. Ruipérez, and D. , A Fourier-Mukai transform for stable bundles on K3 surfaces, J. Reine Angew. Math, vol.486, pp.1-16, 1997.

C. Bartocci, U. Bruzzo, D. Hernández-ruipérez, and M. Jardim, Nahm and Fourier-Mukai transforms in geometry and mathematical physics, 2005.
DOI : 10.1007/b11801

C. Bartocci, U. Bruzzo, D. Hernández-ruipérez, M. Porras, and J. M. , Mirror Symmetry on K3 Surfaces via Fourier-Mukai Transform, Communications in Mathematical Physics, vol.195, issue.1, pp.79-93, 1998.
DOI : 10.1007/s002200050380
URL : http://arxiv.org/abs/alg-geom/9704023

C. Bartocci, U. Bruzzo, D. Hernández-ruipérez, M. Porras, and J. M. , Relatively Stable Bundles over Elliptic Fibrations, Mathematische Nachrichten, vol.98, issue.1, pp.23-36, 2002.
DOI : 10.1002/1522-2616(200205)238:1<23::AID-MANA23>3.0.CO;2-#
URL : http://arxiv.org/abs/math/0109123

A. Basu and S. Sethi, World-sheet stability of (0,2) linear sigma models, Physical Review D, vol.68, issue.2, pp.68-025003, 2003.
DOI : 10.1103/PhysRevD.68.025003

C. Beasley and E. Witten, Residues and world-sheet instantons, Journal of High Energy Physics, vol.17, issue.10, p.pp. (electronic), 2003.
DOI : 10.1016/S0550-3213(02)01093-3
URL : http://arxiv.org/abs/hep-th/0304115

A. Beauville, M. S. Narasimhan, and S. Ramanan, Spectral curves and the generalised theta divisor, J. Reine Angew. Math, vol.398, pp.169-179, 1989.

P. Berglund, P. Candelas, and X. De-la-ossa, Periods for Calabi-Yau and Landau-Ginzburg vacua, Nuclear Physics B, vol.419, issue.2, pp.352-403, 1994.
DOI : 10.1016/0550-3213(94)90047-7
URL : http://doi.org/10.1016/0550-3213(94)90047-7

M. Bershadsky, A. Johansen, T. Pantev, and V. Sadov, On four-dimensional compactifications of F-theory, Nuclear Physics B, vol.505, issue.1-2, pp.165-201, 1997.
DOI : 10.1016/S0550-3213(97)00393-3

M. Bershadsky, C. Vafa, and V. Sadov, D-branes and topological field theories, Nuclear Physics B, vol.463, issue.2-3, pp.420-434, 1996.
DOI : 10.1016/0550-3213(96)00026-0
URL : http://doi.org/10.1016/0550-3213(96)00026-0

A. I. Bondal and D. O. Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences, Compositio Mathematica, vol.125, issue.3, pp.327-344, 2001.
DOI : 10.1023/A:1002470302976

T. Bridgeland, Stability conditions on K3 surfaces. math, p.307164
DOI : 10.1215/s0012-7094-08-14122-5
URL : http://arxiv.org/abs/math/0307164

T. Bridgeland, Stability conditions on triangulated categories. math, 212237.
DOI : 10.4007/annals.2007.166.317
URL : http://arxiv.org/abs/math/0212237

T. Bridgeland, Fourier-Mukai transforms for elliptic surfaces, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.1998, issue.498, pp.115-133, 1998.
DOI : 10.1515/crll.1998.046
URL : http://arxiv.org/abs/alg-geom/9705002

T. Bridgeland, Equivalences of triangulated categories and Fourier-Mukai transforms, Bull, pp.25-34, 1999.

T. Bridgeland, Flops and derived categories, Inventiones Mathematicae, vol.147, issue.3, pp.613-632, 2002.
DOI : 10.1007/s002220100185
URL : http://arxiv.org/abs/math/0009053

T. Bridgeland and A. Maciocia, Fourier-Mukai transforms for K3 and elliptic fibrations, Journal of Algebraic Geometry, vol.11, issue.4, pp.629-657, 2002.
DOI : 10.1090/S1056-3911-02-00317-X
URL : http://arxiv.org/abs/math/9908022

E. Buchbinder, R. Donagi, and B. A. Ovrut, Vector Bundle Moduli and Small Instanton Transitions, Journal of High Energy Physics, vol.12, issue.06, p.44, 2002.
DOI : 10.1002/(SICI)1521-3978(199906)47:6<587::AID-PROP587>3.0.CO;2-5
URL : http://arxiv.org/abs/hep-th/0202084

C. Ald?-araru and A. , Fiberwise stable bundles on elliptic threefolds with relative Picard number one, C. R. Math. Acad. Sci. Paris, vol.334, pp.469-472, 2002.

J. Callan, C. G. Harvey, J. A. Strominger, and A. , Worldbrane actions for string solitons, Nuclear Physics B, vol.367, issue.1, pp.60-82, 1991.
DOI : 10.1016/0550-3213(91)90041-U
URL : http://doi.org/10.1016/0550-3213(91)90041-u

J. Callan, C. G. Harvey, J. A. Strominger, and A. , Worldsheet approach to heterotic instantons and solitons, Nuclear Physics B, vol.359, issue.2-3, pp.611-634, 1991.
DOI : 10.1016/0550-3213(91)90074-8
URL : http://doi.org/10.1016/0550-3213(91)90074-8

P. Candelas, X. De-la-ossa, A. Font, S. Katz, and D. R. Morrison, Mirror symmetry for two-parameter models. I, Nuclear Phys, pp.481-538, 1994.
DOI : 10.1016/0550-3213(94)90322-0
URL : http://doi.org/10.1016/0550-3213(94)90322-0

P. Candelas, X. De-la-ossa, A. Font, S. Katz, and D. R. Morrison, Mirror symmetry for two parameter models. I, in Mirror symmetry, II, pp.483-543, 1997.
DOI : 10.1016/0550-3213(94)90322-0
URL : http://doi.org/10.1016/0550-3213(94)90322-0

P. Candelas, X. De-la-ossa, P. S. Green, and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Physics B, vol.359, issue.1, pp.21-74, 1991.
DOI : 10.1016/0550-3213(91)90292-6

P. Candelas, A. Font, S. Katz, and D. R. Morrison, Mirror symmetry for two-parameter models (I), Nuclear Physics B, vol.416, issue.2, pp.626-674, 1994.
DOI : 10.1016/0550-3213(94)90322-0
URL : http://doi.org/10.1016/0550-3213(94)90322-0

G. Curio, Chiral matter and transitions in heterotic string models, Physics Letters B, vol.435, issue.1-2, pp.39-48, 1998.
DOI : 10.1016/S0370-2693(98)00713-8

P. Deligne, Courbes elliptiques: formulaire d'après J. Tate, in Modular functions of one variable, IV (Proc. Internat. Summer School, pp.53-73, 1972.

D. Diaconescu and G. Ionesei, Spectral covers, charged matter and bundle cohomology, Journal of High Energy Physics, vol.1998, issue.12, 1998.
DOI : 10.1088/1126-6708/1998/12/001
URL : http://arxiv.org/abs/hep-th/9811129

D. Diaconescu and C. Römelsberger, D-branes and bundles on elliptic fibrations, Nuclear Physics B, vol.574, issue.1-2, pp.245-262, 2000.
DOI : 10.1016/S0550-3213(00)00051-1
URL : http://doi.org/10.1016/s0550-3213(00)00051-1

R. Donagi, Taniguchi lectures on principal bundles on elliptic fibrations, in Integrable systems and algebraic geometry, World Sci. Publishing, River Edge, NJ, pp.33-46, 1997.

R. Donagi, A. Lukas, B. A. Ovrut, and D. Waldram, Holomorphic vector bundles and non-perturbative vacua in M-theory, Journal of High Energy Physics, vol.1999, issue.06, p.pp. (electronic), 1999.
DOI : 10.1088/1126-6708/1999/06/034

R. Donagi, B. A. Ovrut, T. Pantev, and D. Waldram, Standard-model bundles, Advances in Theoretical and Mathematical Physics, vol.5, issue.3, pp.563-615, 2001.
DOI : 10.4310/ATMP.2001.v5.n3.a5

R. Donagi, B. A. Ovrut, T. Pantev, and D. Waldram, Standard models from heterotic M-theory, Advances in Theoretical and Mathematical Physics, vol.5, issue.1, pp.93-137, 2001.
DOI : 10.4310/ATMP.2001.v5.n1.a4
URL : http://arxiv.org/abs/hep-th/9912208

M. R. Douglas, D-branes, categories and N=1 supersymmetry, Strings, branes, and M-theory, pp.2818-2843, 2001.
DOI : 10.1063/1.1374448
URL : http://arxiv.org/abs/hep-th/0011017

M. R. Douglas, D-Branes on Calabi-Yau Manifolds, European Congress of Mathematics Progr. Math, vol.202, pp.449-466, 2001.
DOI : 10.1007/978-3-0348-8266-8_39
URL : http://arxiv.org/abs/math/0009209

M. R. Douglas, Dirichlet branes, homological mirror symmetry, and stability, Proceedings of the International Congress of Mathematicians, pp.395-408, 2002.

M. R. Douglas, B. Fiol, and C. Römelsberger, Stability and bps branes. hep-th, 2037.
DOI : 10.1088/1126-6708/2005/09/006
URL : http://arxiv.org/abs/hep-th/0002037

M. J. Duff, R. Minasian, and E. Witten, Evidence for heterotic/heterotic duality, Nuclear Physics B, vol.465, issue.3, pp.413-438, 1996.
DOI : 10.1016/0550-3213(96)00059-4
URL : http://doi.org/10.1016/0550-3213(96)00059-4

R. Friedman, Vector bundles and SO(3)-invariants for elliptic surfaces, J. Amer. Math. Soc, vol.8, pp.29-139, 1995.
DOI : 10.2307/2152883
URL : http://arxiv.org/pdf/alg-geom/9307002v1.pdf

R. Friedman and J. W. Morgan, Smooth four-manifolds and complex surfaces, Mathematics and Related Areas, 1994.
DOI : 10.1007/978-3-662-03028-8

R. Friedman, J. W. Morgan, and E. Witten, Vector Bundles and F Theory, Communications in Mathematical Physics, vol.187, issue.3, pp.679-743, 1997.
DOI : 10.1007/s002200050154
URL : http://arxiv.org/abs/hep-th/9701162

R. Friedman, J. W. Morgan, and E. Witten, Principal $G$-bundles over elliptic curves, Mathematical Research Letters, vol.5, issue.1, pp.97-118, 1998.
DOI : 10.4310/MRL.1998.v5.n1.a8
URL : http://arxiv.org/abs/alg-geom/9707004

R. Friedman, J. W. Morgan, and E. Witten, Vector bundles over elliptic fibrations, J. Algebraic Geom, vol.8, pp.279-401, 1999.
DOI : 10.1007/978-1-4612-1688-9_9

W. Fulton, Intersection theory, Mathematics and Related Areas, 1984.

D. Gieseker, On the Moduli of Vector Bundles on an Algebraic Surface, The Annals of Mathematics, vol.106, issue.1, pp.45-60, 1977.
DOI : 10.2307/1971157

M. B. Green, J. H. Schwarz, and E. Witten, Superstring theory, Cambridge Monographs on Mathematical Physics, vol.1, 1988.
DOI : 10.1017/cbo9781139644228.007
URL : https://hal.archives-ouvertes.fr/jpa-00221917

M. B. Green, J. H. Schwarz, and E. Witten, Superstring theory, Cambridge Monographs on Mathematical Physics, vol.2, 1988.
DOI : 10.1017/cbo9781139644228.007
URL : https://hal.archives-ouvertes.fr/jpa-00221917

B. R. Greene, String theory on Calabi-Yau manifolds, Fields, strings and duality World Sci. Publishing, River Edge, NJ, pp.543-726, 1996.

A. Grothendieck, ´ Eléments de géométrie algébrique. III. ´ Etude cohomologique des faisceaux cohérents . I, Inst, HautesÉtudesHautes´HautesÉtudes Sci. Publ. Math, vol.167, 1961.

R. Hartshorne, Residues and duality, With an appendix by P. Deligne, Lecture Notes in Mathematics, vol.20, 1966.

R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, vol.52, 1977.
DOI : 10.1007/978-1-4757-3849-0

J. A. Harvey and G. Moore, On the Algebras of BPS States, Communications in Mathematical Physics, vol.197, issue.3, pp.489-519, 1998.
DOI : 10.1007/s002200050461

H. Ruipérez, D. , M. Porras, and J. M. , Stable sheaves on elliptic fibrations, Journal of Geometry and Physics, vol.43, issue.2-3, pp.163-183, 2002.
DOI : 10.1016/S0393-0440(02)00019-0

N. J. Hitchin, The Self-Duality Equations on a Riemann Surface, Proc. London Math. Soc. (3), pp.59-126, 1987.
DOI : 10.1112/plms/s3-55.1.59

P. Horja, Derived category automorphisms from mirror symmetry, Duke Mathematical Journal, vol.127, issue.1
DOI : 10.1215/S0012-7094-04-12711-3
URL : http://arxiv.org/abs/math/0103231

S. Hosono, GKZ systems, Gröbner fans, and moduli spaces of Calabi-Yau hypersurfaces, in Topological field theory, primitive forms and related topics, Progr. Math, vol.160, pp.239-265, 1996.

S. Hosono, A. Klemm, S. Theisen, and S. Yau, Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nuclear Physics B, vol.433, issue.3, pp.501-552, 1995.
DOI : 10.1016/0550-3213(94)00440-P
URL : http://doi.org/10.1016/0550-3213(94)00440-p