Here we introduce the concept of special effect curve which permits to study, from a different point of view, special linear systems in P^2, i.e., linear system with general multiple base points whose effective dimension is strictly greater than the expected one. In particular we study two different kinds of special effect: the α-special effect is defined by requiring some numerical conditions, while the definition of h1-special effect concerns cohomology groups. We state two new conjectures for the characterization of special linear systems and we prove they are equivalent to the Segre and the Harbourne-Hirschowitz ones.

Bocci, C. (2010). Special effect varieties and (-1)-curves. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 40(2), 397-419 [10.1216/RMJ-2010-40-2-397].

Special effect varieties and (-1)-curves

BOCCI, CRISTIANO
2010

Abstract

Here we introduce the concept of special effect curve which permits to study, from a different point of view, special linear systems in P^2, i.e., linear system with general multiple base points whose effective dimension is strictly greater than the expected one. In particular we study two different kinds of special effect: the α-special effect is defined by requiring some numerical conditions, while the definition of h1-special effect concerns cohomology groups. We state two new conjectures for the characterization of special linear systems and we prove they are equivalent to the Segre and the Harbourne-Hirschowitz ones.
Bocci, C. (2010). Special effect varieties and (-1)-curves. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 40(2), 397-419 [10.1216/RMJ-2010-40-2-397].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/12411
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