G. Occhetta, L.E. Solá Conde and J. Wisniewski

Flag bundles on Fano manifolds,

to appear in Journal de Mathématiques Pures et Appliquées


G. Occhetta, L.E. Solá Conde and K. Watanabe

Uniform families of minimal rational curves on Fano manifolds,

to appear in Revista Matematica Complutense


R. Muñoz, G. Occhetta, L.E. Solá Conde, K. Watanabe and J. Wisniewski

A survey on the Campana-Peternell Conjecture

Rendiconti dell'Istituto di Matematica dell'Università di Trieste 47, (2015) 127-185


G. Occhetta, L.E. Solá Conde and K. Watanabe and J. Wisniewski

Fano manifolds whose elementary contractions are smooth P1-fibrations

to appear in Annali Sc. Norm. Super. Pisa Cl. Sci.


R. Muñoz, G. Occhetta, L.E. Solá Conde and K. Watanabe

Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle.

Math. Ann., 361, (2015), 583-609


R. Muñoz, G. Occhetta and L.E. Solá Conde

A classification theorem for Fano bundles.

Annales Inst. Fourier 64 (2014), no. 1, 341-373.


R. Muñoz, G. Occhetta and L.E. Solá Conde

On rank 2 vector bundles on Fano manifolds.

Kyoto Journal of Mathematics 54 (2014), no. 1, 167-197.


C. Novelli, G. Occhetta

Manifolds covered by lines and extremal rays.

Canad. Math. Bull. 55 (2012), no. 4, 799–814.


R. Muñoz, G. Occhetta and L.E. Solá Conde

Rank two Fano bundles on G(1,4).

Journal of Pure and applied Algebra, 216, (2012), 2269-2273


  1. G.Occhetta, V. Paterno

Rationally cubic connected manifolds II.

Revista Mathemática Iberoamericana, 28, (2012), 815-838


  1. G.Occhetta, V. Paterno

Rationally cubic connected manifolds I: manifolds covered by lines.

J. Math. S



Gians' page

On Hartshorne's book


Chapter 1: Euclid's Geometry

  1. 1. A first look at Euclid's elements - done

  2. 2. Ruler and compass contructions - done

  3. 3. Euclid's axiomatic method - done

  4. 4. Construction of the regular pentagon - done


Chapter 2: Hilbert's Axioms

  1. 6.Axioms of incidence - done

7. Axioms of betweenness - done

8. Axiom of congruences for line segments - done

9. Axiom of congruences for angles - done

  1. 10.Hilbert planes - done

  2. 11.Intersection of lines and circles - done

  3. 12. Euclidean planes - done


Chapter 3: Geometry over fields


    Quick Overview


Chapter 4: Segment arithmetic

  1. 19.Addition and multiplication... - done

  2. 20.Similar triangles - done



Chapter 7: Noneuclidean Geometries

  1. 33.History of the parallel postulate - done

  2. 34.Neutral geometry - done

  3. 35.Archimedean neutral geometry - done

37. Circular inversion - done

  1. 39.The Poincaré model - done

  2. 40.Hyperbolic geometry - done


Euclid's Elements


Book I-IV Definitions and Propositions


Book I:   Everything


Book II:  Prop. 4-6, 11 and 14


Book III: Prop. 1, 3, 9, 17,

          20-22, 31-32, 35-37


Book IV: Prop. 1-5, 10-11, 15

Published papers

FOUNDATIONS OF GEOMETRY



COURSE DIARY



BIBLIOGRAPHY




SELECTED EXERCISES

Section 1  1.4 - 1.10, 1.12 - 1.14

Section 2  2.1 - 2.18, 2.24

Section 3  3.3 - 3.9

Section 6  6.5a, 6.5b, 6.8

Section 7  7.4, 7.9, 7.10, 7.14

Section 8  8.2, 8.3, 8.5, 8.7

Section 9  9.1, 9.2, 9.4

Section 10  10.1 - 10.5, 10.11

Section 11  11.1 - 11.5, 11.5

Section 17  17.3

Section 20  20.1 - 20.3, 20.10

Section 34  34.1, 34.4, 34.9, 34.10

Section 37  37.2, 37.3

Section 40  40.1 - 40.5

Published papers








CONSTRUCTIONS WITH GEOGEBRA




SELECTED PROPOSITIONS FROM EUCLID'S ELEMENTS

Book I     5, 6, 16, 18, 20, 21, 26, 27, 29, 43, 47

Book II    4, 5, 6, 11, 14

Book III   20, 22, 31, 32, 35-37

Book IV    2, 3, 10, 11







  Next written examinations:

 

  June 11 - 9.30

  July 15 - 9.30

  August 30 - 9.30



Exercise sheets











    Exercise Sheet 1 (due Thursday, March 7)

    Exercise Sheet 2 (due Thursday, March 21)

    Exercise Sheet 3 (due Thursday, April 4)

    Exercise Sheet 4 (due Thursday, April 18)

    Exercise Sheet 5 (due Thursday, May 2)

    Exercise Sheet 6 (due Thursday, May 16)