LibreTimes

Search results for “complete intersections”

14 results

The torsion component of the Picard scheme

2026OtherBogdan Zavyalov

Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.
1
500

IMO 1965

2026Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
0
320

A curiosity: “supersmooth” varieties

2026TheorySean Cotner

A rigidity condition on schemes, strictly stronger than smoothness, introduced with examples and a look at where it fails to be geometric — no known application, just a curiosity.
1
120

An example of a non-reduced Picard scheme

2026TheorySean Cotner

An example, due to Serre, of a smooth projective surface in positive characteristic whose Picard scheme fails to be reduced, worked out via the two governing dimension inequalities.
1
170

Some examples of algebraic groups

2026TheorySean Cotner

Two pathological phenomena for algebraic groups over general bases — a group degenerating between the multiplicative and additive group across a DVR, and a non-affine identity component — built as centralizers in SL_n.

0
180

Properties of Matrix Operations

2026TheorySergey

The basic properties of addition, scalar multiplication, transposition, and multiplication of matrices, with justifications.
0
180

IMO 1976

2026Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
0
260

Inverse Matrices

2026TheorySergey

Nonsingular matrices, the invertibility criterion, the adjugate-matrix formula, and the Gauss–Jordan method.
0
120

Linear (Vector) Space

2026TheorySergey

The axioms of a linear (vector) space, examples and counterexamples.
0
160

The Steinberg Representation

2026TheorySean Cotner

An introduction to the Steinberg representation of a finite group of Lie type — its alternating-sum construction from parabolic inductions, worked out explicitly for SL_2.

0
270

IMO 2014

2026Problem sheet

55th International Mathematical Olympiad. Cape Town, South Africa, 2014.
0
330