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| 04/12/2025 | 14h00 (salle W, esc B 4ème étage) à l'ENS | Grigory Mikhalkin,
Totally real rational functions of degree g on real curves of genus g |
| | Abstract. A real function is totally real if the inverse image of any real value consists entirely of real points. Such a function gives an (unramified) covering of a real curve over the circle. Kummer and Shaw have introduced the "separating semigroup" of a real curve as all possible multidegrees appearing in this way. We overview what is known on this semigroup, paying a special attention to the elements of degree equal to the genus of the curve. Based on a joint work with Stepan Orevkov. |
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| 11/12/2025 | 14h00 (15-25 101) !!Jussieu!! | Andreas Höring,
Nonvanishing results for Kähler varieties |
| | Let X be a simply-connected compact Kähler (or complex projective) manifold with first Chern class equal to zero, and let L be a "semi positive" line bundle on X. The non-vanishing problem for K-trivial varieties asks if some multiple of L has a global section. This problem is very difficult and open even for Calabi-Yau threefolds. In this talk I will present joint work with Vlad Lazic and Christian Lehn where we exhibit some geometric obstructions for the existence of such a section and show non-vanishing results for varieties where the Euler characteristic does not vanish. |
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| 18/12/2025 | 14h00 (salle W, esc B 4ème étage) à l'ENS | John Lesieutre,
Volume near the pseudoeffective boundary |
| | Abstract: Suppose that X is a projective variety and that L is a line bundle on X. The volume of L is a measure of the asymptotic growth rate of the number of sections of tensor powers of L. After providing some background on this invariant, I will explain some pathological behaviors of the volume function which have origins in the dynamics of birational automorphisms of a certain Calabi-Yau threefold X. |
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