Lecture
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07 Mar 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Introduzione al corso. Esempi di problemi enumerativi. Cicli su varietà, e gruppi di Chow. La successione di omotopia.
08 Mar 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Funtorialità dei gruppi di Chow: pushforward proprio e pullback piatto.
14 Mar 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Compatibilità tra pushforward proprio e pullback piatto. Esempi.
15 Mar 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Anelli di Chow di varietà lisce. Anelli di Chow di spazi proiettivi. Formula di proiezione. Esempi. Il grado di una varietà di Veronese.
04 Apr 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Online
Anelli di Chow di prodotti. Grado dell'immersione di Segre. Soluzioni di problemi enumerativi per curve piane riducibili.
05 Apr 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Grado della varietà discriminante. Fibrati vettoriali e loro proiettivizzazioni.
11 Apr 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Chern classes and their properties. Examples and applications.
12 Apr 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Proof of the splitting principle, and of the multiplicativity of Chern classes. Grassmanianns: definitions, and first properties.
18 Apr 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Schubert cycles, and Schubert cells. The Chow ring of G(2,4).
26 Apr 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
The Chow ring of the Grassmannian G(2,4).
02 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
27 lines on a cubic surface.
03 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Chow rings of general Grassmannians. Intersection of Schubert cycles in complementary dimension. Pieri's rule. Giambelli's formula. Examples.
09 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Chern classes of the tautological and the quotient bundles on Grassmannians. Linear subspaces on quadrics.
10 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Preparazione ore lezioni - Products of Schubert cycles on G(2,n). Degree of the Plücker embedding of G(2,n). Fano varieties of lines; general setup.
16 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
The universal Fano variety. The class of the universal Fano variety in the product of the Grassmannian with projective space. 2875 lines on a quintic threefold. The degree of the variety of quartic surfaces in P^3 containing a line is 320.
17 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
The number of conics on a general quintic threefold. Hilbert schemes: definition and first properties. The Grassmannian as a Hilbert scheme.
23 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Hilbert schemes of hypersurfaces. Tangent spaces to a scheme.
24 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Linear functors and functors preserving finite products. Tangent spaces to Grassmannians and Hilbert schemes.
30 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
Properties of normal bundles. Fano schemes of lines. Tangent spaces to Fano schemes, and applications.
31 May 2024 (2h 00m)
Angelo Vistoli - Course (teaching activity) - Both face to face and online
The main theorem on tangent spaces to Fano varieties of lines on hypersurfaces.
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