Embeddings of general blowups of abelian surfaces

Blowups of algebraic surfaces polarized by tensor powers of ample line bundles were studied by Coppens [8]. In this note we complete the picture in the case of abelian surfaces studying blowups of surfaces polarized by primitive line bundles. Received: 16 November 1999 / Revised version: 13 June 2000     

On 3-syzygy and unexpected plane curves

Geometriae Dedicata - We prove a new inequality relating volume to length of closed geodesics on area minimizers for generic metrics on the complex projective plane. We exploit recent regularity...     

Highly stereoselective synthesis of 2-deoxy-α- glycosides and α-disaccharides

Highly stereoselective synthesis of 2-deoxy-α-glycosides including disaccharides is described, using S-(2-deoxyglycosyl)phosphorodithioates as glycosyl donors, in the presence of silver perchlorate in acetonitrile     

NEW NATURAL SULFOXIDES OF NUPHAR ORIGIN. STRUCTURE,CHEMISTRY, PUMMERER REARRANGEMENT

Abstract

Further studies on basic compounds from Nuphar luteum L. Sm. resulted in isolation of a new group of sulfoxides with thiohemiaminal type of structure.     

Ortho- and para-substituted Hoveyda-Grubbs carbenes. An improved synthesis of highly efficient metathesis initiators

A novel highly efficient and general route to various 3- and 5-substituted 2-alkoxystyrenes, required for the preparation of Hoveyda-Grubbs catalysts, is described.     

Linear subspaces,symbolic powers and Nagata type conjectures

Inspired by results of Guardo, Van Tuyl and the second author for lines in P³${\mathbb{P}}^3$, we develop asymptotic upper bounds for the least degree of a homogeneous form vanishing to order at least m on a union of disjoint r  -dimensional planes in Pⁿ${\mathbb{P}}^n$ for n?2r+1$n?2r+1$. These considerations lead to new conjectures that suggest that the well known conjecture of Nagata for points in P²${\mathbb{P}}^2$ is not an exotic statement but rather a manifestation of a much more general phenomenon which seems to have been overlooked so far.     

First Stereqselective Synthesis of Nitrophenyl 2-Deoxy- β-D-glycosides

α-Dithiophosphates of peracetylated 2-deoxyhexc-pyranoses, 1a, 1b and 2, uhich are easily prepared by addition of organic phosphorodithioic acids to glycais react smoothly with resin-bound 2- and 4-nitrophenoxides to give stereoselectively the respective nitrophenyl 2-deoxy-β-D-hexopyranosides (3, 4, 5 and 6) in high yields. Glycosylation of the 2, 4-dinitro'phenoxide, however, leads with comparable stereoselectivity to 2,4-dinitrophenyl 2-deoxy- α-D-hexopyranosides (7 and 8).

Glycosides 3 - 6 are quantitatively deacetylatec by Amberlyst A-26 (OH^-), whereas glycosides 7 and 8, under the same reaction conditions undergo splitting of the O-glycosidic bond.     

Seshadri constants in two half-periods

We calculate the exact value of the multiple point Seshadri constant in two halfperiods of an abelian surface with Picard number one. Received: 3 December 2003; revised: 9 July 2005     

A note on general blow-ups of abelian surfaces

In the paper we give numerical conditions for a line bundle on a general blow-up of abelian surface to be k-very ample.