1,248 research outputs found
The wronskian and its derivatives
Articolo testo di una conferenza tenuta presso l'Accademia Peloritana dei Pericolanti (Messina
Jet bundles on Gorenstein curves and applications
In the last twenty years a number of papers appeared aiming to construct
locally free replacements of the sheaf of principal parts for families of
Gorenstein curves. The main goal of this survey is to present to the widest
possible audience of mathematical readers a catalogue of such constructions,
discussing the related literature and reporting on a few applications to
classical problems in Enumerative Algebraic Geometry.Comment: Minor revisions, improved expositio
Limits of special Weierstrass points
Let C be the union of two general connected, smooth, nonrational curves X and
Y intersecting transversally at a point P. Assume that P is a general point of
X or of Y. Our main result, in a simplified way, says:
Let Q be a point of X. Then Q is the limit of special Weierstrass points on a
family of smooth curves degenerating to C if and only if Q is not P and either
of the following conditions hold: Q is a special ramification point of the
linear system |K_X+(g_Y+1)P|, or Q is a ramification point of the linear system
|K_X+(g_Y+1+j)P| for j=-1 or j=1 and P is a Weierstrass point of Y.
Above, g_Y stands for the genus of Y and K_X for a canonical divisor of X.
As an application, we recover in a unified and conceptually simpler way
computations made by Diaz and Cukierman of certain divisor classes in the
moduli space of stable curves. In our method there is no need to worry about
multiplicities, an usual nuisance of the method of test curves.Comment: 33 pages, 4 figure
Special ramification loci on the double product of a general curve
Let C be a general connected, smooth, projective curve of positive genus g.
For each nonnegative integer i we give formulas for the number of pairs (P,Q)
em C x C off the diagonal such that (g+i-1)Q-(i+1)P is linearly equivalent to
an effective divisor, and the number of pairs (P,Q) em C x C off the diagonal
such that (g+i+1)Q-(i+1)P is linearly equivalent to a moving effective divisor.Comment: 32 pages, 1 figur
- ā¦