ar X iv : 0 70 7 . 46 02 v 2 [ m at h . A G ] 2 2 O ct 2 00 7 Geometry of the Theta Divisor of a compactified Jacobian

ar X iv : 0 70 7 . 46 02 v 3 [ m at h . A G ] 3 M ay 2 00 8 Geometry of the Theta Divisor of a compactified Jacobian

The object of this paper is the theta divisor of the compactified Jacobian of a nodal curve. We determine its irreducible components and give it a geometric interpretation. A characterization of hyperelliptic irreducible stable curves is appended as an application.

ar X iv : 0 70 7 . 40 46 v 1 [ m at h . A G ] 2 7 Ju l 2 00 7 CLIFFORD ’ S THEOREM FOR COHERENT SYSTEMS

Let C be an algebraic curve of genus g ≥ 2. We prove an analogue of Clifford’s theorem for coherent systems on C and some refinements using results of Re and Mercat.

ar X iv : 0 70 4 . 35 30 v 2 [ m at h . D G ] 2 5 O ct 2 00 7 Invariant forms , associated bundles and Calabi - Yau metrics

We develop a method, initially due to Salamon, to compute the space of " invariant " forms on an associated bundle X = P ×G V , with a suitable notion of invariance. We determine sufficient conditions for this space to be d-closed. We apply our method to the construction of Calabi-Yau metrics on T CP 1 and T CP 2 .

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : h ep - p h / 02 07 09 7 v 1 6 J ul 2 00 2 Remarks on the compactified six - dimensional model of a particle

Non-homogeneous gauge ground state solutions in a six-dimensional gauge model in the presence of non-zero extended fermionic charge density fluctuations are reviewed and fully reinterpreted.