fano3fold

Documentation

Index

• Constants
• func Degree(g int, B *basket.Points) *rational.Element
• func HilbertSeries(g int, B *basket.Points, precision int) (*integerpolynomial.Element, *rational.Element)
• func Kc2(B *basket.Points) *rational.Element
• type Variety
  • func New(g int, B *basket.Points) (*Variety, error)
  • func (X *Variety) AssignWeights(W []int)
  • func (X *Variety) Basket() *basket.Points
  • func (X *Variety) Codimension() int
  • func (X *Variety) Degree() *rational.Element
  • func (X *Variety) Genus() int
  • func (X *Variety) HilbertCoefficients(n int) []*integer.Element
  • func (X *Variety) HilbertNumerator() *integerpolynomial.Element
  • func (X *Variety) HilbertSeries() *integerpolynomial.Element
  • func (X *Variety) Kc2() *rational.Element
  • func (X *Variety) String() string
  • func (X *Variety) Weights() []int

Constants

const Precision = 100

Functions

func Degree

func Degree(g int, B *basket.Points) *rational.Element

Degree returns the degree -K_X^3 of an index 1 Fano 3-fold X with genus g and basket B = [ [r,a], ... ]

func HilbertSeries

func HilbertSeries(g int, B *basket.Points, precision int) (*integerpolynomial.Element, *rational.Element)

Hilbert series returns the Hilbert series of an index 1 Fano 3-fold with genus g and basket B = [ [r,a], ... ]; the degree is returned as a second value.

func Kc2

func Kc2(B *basket.Points) *rational.Element

Kc2 returns the rational number -K_X*c2(X) of an index 1 Fano 3-fold X with basket B = [ [r,a], ... ]

Types

type Variety

type Variety struct {
	// contains filtered or unexported fields
}

Variety contains the numerical data that represents a Fano 3-fold.

func New

func New(g int, B *basket.Points) (*Variety, error)

New creates a Fano 3-fold with genus g and basket B

func (*Variety) AssignWeights

func (X *Variety) AssignWeights(W []int)

AssignWeights sets the weights to W (and clears the Hilbert numerator)

func (*Variety) Basket

func (X *Variety) Basket() *basket.Points

Basket returns the basket of X

func (*Variety) Codimension

func (X *Variety) Codimension() int

Codimension returns the codimension of X

func (*Variety) Degree

func (X *Variety) Degree() *rational.Element

Degree returns the degree of X

func (*Variety) Genus

func (X *Variety) Genus() int

Genus returns the genus g of X

func (*Variety) HilbertCoefficients

func (X *Variety) HilbertCoefficients(n int) []*integer.Element

HilbertCoefficients returns the coefficients Hilbert series of X, starting with the constant coefficient and ending with the coefficient of x^(n-1)

func (*Variety) HilbertNumerator

func (X *Variety) HilbertNumerator() *integerpolynomial.Element

HilbertNumerator returns the numerator of the Hilbert series of X w.r.t the weights.

func (*Variety) HilbertSeries

func (X *Variety) HilbertSeries() *integerpolynomial.Element

HilbertSeries returns the Hilbert series of X (currently as poly which is leading portion of power series).

func (*Variety) Kc2

func (X *Variety) Kc2() *rational.Element

Kc2 returns the rational number K_X * c_2(X)

func (*Variety) String

func (X *Variety) String() string

String returns Fano 3-fold X as a string

func (*Variety) Weights

func (X *Variety) Weights() []int

Weights returns the weights of X if assigned