Concept

Projective space

Related lectures (29)

Covers invariants and dimensions of projective varieties, emphasizing their importance.

Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.

Covers the concept of connected sums in RP2 and how to compute them.

Explores singular points, the group law, and the ambiguity in defining the sum of a point with itself on elliptic curves.

Explores the complement problem for hypersurfaces in projective spaces and discusses isomorphism based on their complements.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

Covers the homology of projective space, focusing on cohomology and exact sequences.

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Explores automorphisms of projective varieties, discussing isomorphism between complements and key observations on dimensions and examples.

Explores projective algebraic sets, prime ideals, irreducible sets, cones, and Nullstellensatz theorem.

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Covers the study of projective varieties and their relation to compact manifolds.

Explores the Cayley-Bacharach theorem in incidence geometry and introduces elliptic curves with a commutative law.

Explores modern symmetry in geometry, covering transformations, isometries, orientations, and practical applications.

Explores the harmonic mean in visual arts and projective geometry, discussing historical context and invariance properties.

Explores traditional stone cutting and assembly techniques, geometric modeling, and the historical development of projective geometry in stereotomy.

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.

Explores the historical development of projective geometry and the contributions of key figures like Alberti and Piero della Francesca.