Projective Geometry with Applications

Remarks on numerically positive and big line bundles; order-sequences and rational curves; classification of smooth congruences with a fundamental curve; on a result of Zak-L'vosky; trisecant formulas for smooth projective varieties; derived triangles and differential systems; computing gaps sequences at Gorenstein singularities; on the Weierstrass weights at Gorenstein singularities; Weierstrass Loci and generalizations; a problem of trigonality for some Fano varieties; families of singular meromorphic foliations; on stable sheaves on algebraic surfaces; cohomology of generic rank 2 stable bundles on Fano 3-folds of index 2; linear series of low degree on plane curves and the Castelnuovo function; rational curves on Calabi-Yau manifolds - verifying prediction of mirror symmetry. (Part contents).