(270) Marlowe's "Hero and Leander" and Shakespeare's "Lucrece" must have sprung from a single brain.....

its unlikely, that a highly specific poetic thought within a year has sprung from 2 separate "brains".

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The poetic-erotic thought  in Marlowe's "Hero and Leander" (1593) and  in Shakespeare's "Lucrece" (1594) is quoted here: it  supports the idea of ​​an  identity of both persons :

basically,  its unlikely, that this poetic thought within a year  has sprung from 2 separate "brains".     

"Hero and Leander" (Marlowe) 1593     

        "For though the rising iv'ry mount he scaled               

          Which is with azure circling lines empaled                 

          Much like a globe " 

 "Lucrece"  (Shakespeare) 1594
          "Her breasts as ivory globes circled with blue
           A pair of maiden worlds unconquered. 

"Shakespeare repeats Marlowe's content with similar terms: "azure" / "blue", -  "female breast" / "ivory globe"   -  or "globe" / "world".  

Both convey "verses" that the female breast remember two ivory balls / globes and that they are surrounded by a blue stain. *1)

Picture out of Charles Sorel
/John Davies "The Extravagant
 Shepheard"(1653/1660)

Marlowe's misconduct and crash  first and foremost was , that  - in the  spring of 1593 -  he  was considered the author or contributor of the circulating leaflets ("libels") held in verse, signed with "Tamburlaine". (-> »Dutch Libels".  One can assume Marlowe wrote them!). 

Marlowe was accused of high "treason", "rebellion" and "sedition", an accusation which was punishable by death. 

Queen Elizabeth must have regarded Marlowe as the initiator of the Libel texts. Influential circles should Elisabeth have asked to condemn him to death (not primarily - as commonly believed- because of Marlowe's atheistic heretical views). 

Without this background,  questions what motives could have prompted Shakespeare alias Marlowe  to start his poetic work  with the metaphor of "Lucrece" and "Hero" (associated to Tarquin and Leander) cannot be answered adequately.

The poem "Lucrece", Shakespeare's op.2 is the "real" op.1, the first new creation of Marlowe after his life catastrophy under his new dramatist pseudo-name William Shake-speare *2). -
  "Lucrece" is his acute metaphoric literary treatment of his serious misconduct towards Lucrece (the Queen) ...Tarquinius (Marlowe) had "tar"red the "queen".....

*1) Picture out of Charles Sorel/John Davies "The Extravagant Shepheard"(1653/1660)
*2) "Venus and Adonis" Shakespeare's opus 1 was a prefabricated private work to William Cecil ,