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Lie description of higher obstructions to deforming submanifolds

Marco Manetti (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

To every morphism χ : L M of differential graded Lie algebras we associate a functors of artin rings Def χ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of χ . Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kähler manifold is annihilated by the semiregularity map.

Limit Weierstrass schemes on stable curves with 2 irreducible components

Marc Coppens, Letterio Gatto (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We are concerned with limits of Weierstrass points under degeneration of smooth curves to stable curves of non compact type, union of two irreducible smooth components meeting transversely at m 1 points. The case m = 1 having already been treated by Eisenbud and Harris in [8], we analyze the situation for m > 1 .

Linearly Normal Curves in P^n

Pasarescu, Ovidiu (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In the present paper we apply...

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