HORARIO:
Lunes 5: de 16:00 a 18:30 horas
Martes 6: de 15:15 a 17:45 horas
Jueves 8: de 15:15 a 17:45 horas
Viernes 9: de 11:00 a 13.30 horas
A. SINGULARITIES OF PLANE CURVES
I. Newton trees associated to singularities of plane curves.
1) Newton polygons
2) Newton algorithm
3) Construction of Newton trees
4) Combinatorial properties
II. Intersection multiplicity
1) Curvettes
2) Branches
3) Intersection multiplicity of germs
4) Milnor number
Lectures:
-Singular points of plane curves. C.T.C.Wall (3.1, 3.2, 3.3, 4.3)
Complementary Lectures
-Cassou-Nogues, Libgober : Multivariable Hodge theatrical invariants of germs of plane curves II (section 2.3)
-Cassou-Nogues, Veys : Newton trees for ideals in two variables and applications (section 2.3)
B. BERNSTEIN POLYNOMIAL OF SINGULARITIES OF PLANE CURVES
I. Residues of integrals
1) Meromorphic integrals
2) Residues of integrals
II Applications to the Bernstein Polynomial
1) Link between Bernstein polynomial and integrals.
2) Computation of some generic Bernstein polynomials.
Lectures:
A primer of algebraic D-modules, S.C. Coutinho (Chapter 3)
Artal Bartolo, Cassou-Noguès, Luengo, Melle-Hernandez:
-Yano's conjecture for 2-Puiseux pairs irreducible plane curve singularities
- Bernstein polynomial of 2-Puiseux pairs irreducible plane curve
- On the b-exponents of generic isolated plane curve singularities
Cassou-Noguès:
-Racines de polynômes de Bernstein
-Etude du comportement du polynôme de Bernstein lors d'une déformation à nombre de Milnor constant de X^a+Y^b avec (a,b)=1
-Polynôme de Bernstein générique.
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