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A266322 Genera of complete intersection curves. 1
0, 1, 3, 4, 5, 6, 9, 10, 13, 15, 16, 17, 19, 21, 25, 28, 31, 33, 36, 37, 41, 45, 46, 49, 51, 55, 61, 64, 65, 66, 73, 76, 78, 81, 85, 91, 97, 99, 100, 101, 105, 106, 109, 113, 120, 121, 129, 136, 141, 144, 145, 148, 153, 161, 163, 166, 169, 171, 176, 181, 190 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Pieter Belmans, Table of n, a(n) for n = 1..215

P. Deligne and N. Katz, Groupes de monodromie en géométrie algébrique (SGA 7 II), Springer-Verlag, 1973, pages 39-61.

PROG

(Sage)

def genus(degrees):

  n = len(degrees) + 1

  return 1 + 1 / 2 * prod(degrees) * (sum(degrees) - n - 1)

"""

Generate a list of all genera of complete intersection curves up to a cutoff.

Observe that the genus strictly increases if we increase the degree of a defining equation, while adding a hyperplane section keeps the degree fixed.

So we can obtain all low genera starting from the line in P^2, and increasing the number of equations and the degrees of the defining equations

"""

def listOfGenera(cutoff):

  queue = [(1, )]

  genera = []

  while len(queue) > 0:

    degrees = queue.pop()

    g = genus(degrees)

    if g < cutoff:

      # if we haven't found this one yet we add it to the list

      if g not in genera:

        genera.append(g)

        # use this to get information on how to realize a curve

        # print (g, degrees)

      # add all valid (d_1, ..., d_i+1, ..., d_{n-1})

      for i in range(len(degrees)):

        new = list(degrees)

        new[i] = new[i] + 1

        # we only look at increasing lists of degrees

        if sorted(new) == new:

          queue.append(tuple(new))

      # add (d_1, ..., d_{n-1}, 2): with , 1 at the end genus is constant

      queue.append(degrees + (2, ))

  return sorted(genera)

CROSSREFS

Sequence in context: A129948 A050414 A342469 * A136681 A206330 A104373

Adjacent sequences:  A266319 A266320 A266321 * A266323 A266324 A266325

KEYWORD

nonn

AUTHOR

Pieter Belmans, Dec 27 2015

STATUS

approved

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Last modified September 18 11:20 EDT 2021. Contains 347518 sequences. (Running on oeis4.)