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Rational projectively Cohen-Macaulay surfaces of maximum degree.

Marina Mancini (2001)

Collectanea Mathematica

In this paper we determine the greatest degree of a rational projectively Cohen-Macaulay (p.C.M.) surface V in PN and we study the surfaces which attain such maximum degree.

Relations in the canonical algebras on surfaces

Kazuhiro Konno (2008)

Rendiconti del Seminario Matematico della Università di Padova

Semipolarized nonruled surfaces with sectional genus two.

Biancofiore, Aldo, Fania, Maria Lucia, Lanteri, Antonio (2006)

Beiträge zur Algebra und Geometrie

Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in $ℝ^{3}$

M. Burak Erdoğan, Michael Goldberg, Wilhelm Schlag (2008)

Journal of the European Mathematical Society

We present a novel approach for bounding the resolvent of $H = - Δ + i (A \cdot \nabla + \nabla \cdot A) + V = : - Δ + L 1$ for large energies. It is shown here that there exist a large integer $m$ and a large number $λ_{0}$ so that relative to the usual weighted $L^{2}$ -norm, $∥ {(L {(- Δ + (λ + i 0))}^{- 1})}^{m} ∥ < \frac{1}{2} 2$ for all $λ > λ_{0}$ . This requires suitable decay and smoothness conditions on $A, V$ . The estimate (2) is trivial when $A = 0$ , but difficult for large $A$ since the gradient term exactly cancels the natural decay of the free resolvent. To obtain (2), we introduce a conical decomposition of the resolvent and then sum over...