The shroud is a medieval fake. This has been well established by scientific testing (chemical, microscopic, spectroscopic and radioisotopic), expert examination (textile, weave and artistic style) and historical research (comparison to others, culture and documentation) and is supported by other evidence:
Historical: the lack of evidence for the shroud's existence prior to the mid fourteenth century; further it's emergence during the 'holy relic' craze (along with about forty other such burial shrouds); lack of mention of a miraculously imaged Shroud in any early Christian writings; the distinct changes in the shroud, fading of colour, since its first exposure.
Physiological: the lack of resemblance of the shroud image to an actual human body; likewise the position of the body with hands folded across the genitals isn't possible for a bo.dy lying flay (the arms aren't long enough).
Textile: the weave patten of the shroud does not match anything known from first century Mid East but matches medieval Europe well; no example of the complex herringbone twill weave has even been shown to come from the first century Mid East.
Testimony: the d'Arcis Memo indicates the shroud was created around 1354 and was a known fake not many year later.
Artistic: the face of the image resembles medieval Byzantine style, with Gothic elements; the unnaturally elongated body shape and extremities are typical of the elongated style the Late Medieval/High Gothic period.
Reproducibility: contrary to the claims of shroudies the image can and has been reproduced using medieval methods.
Analytic: examination, microscopic (including electron microscopy) and chemical testing show the shroud image is made from common artistic pigments of the period of its origin.
Cultural: the shroud does not match with what is known of first century Jewish burial practices or the only extant sample of such burial cloths; nor does the shroud match the biblical accounts; nor are there any demonstrated artifacts of the putative Jesus extant today; nor does the supposed historical background indicate that such a cloth would have been preserved, certainly without much publicity prior to ~1355.
Serological: a minor point (as blood probably wouldn't survive this long anyway) but despite the best attempts of (and much lying and pseudoscience by) shroudies there is no evidence for blood residue.
Frankly the consensus of all the factors is the strongest reason to accept the medieval origin of the shroud, not any one factor.